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This comment pertains to the novel modified sub-ODE method introduced in the aforementioned paper. We have established, through a straightforward calculation, that the method employed in the paper is flawed. Moreover, certain exact solutions, as presented in the paper, are also erroneous in the context of both the auxiliary equation method associated with the aforementioned method and the model under investigation, namely the nonlinear low-pass electrical transmission lines model. It is noteworthy that the authors of the paper have asserted on two occasions that they meticulously validated all derived solutions by re-substituting them into the relevant equations, utilizing the Mathematica software. [ABSTRACT FROM AUTHOR]

Some serious errors exist in the above paper. [ABSTRACT FROM AUTHOR]

Aiming at the problem that speech information has a strong correlation in adjacent times and the data type is floating point, the image encryption algorithm of integer type is not suitable for speech encryption. This paper proposed a speech encryption algorithm based on robust chaotic mapping, which mainly utilizes the nonlinearities and dynamics of robust chaos to adapt to the characteristics of speech signals. Furthermore, a new 3D sine robust chaotic mapping (3D-SRCM) model is proposed in this paper, which effectively solves the problems of discontinuous parameter ranges, prone to chaotic degradation and lack of robustness in existing chaotic systems, and improves the robustness and complexity of chaos. In the speech encryption algorithm, the parameters of the chaotic mapping are adjusted according to the changes in speech signal characteristics to generate unique keys for different speech signals. The encryption algorithm compresses and denoises the signal through the Fast Walsh–Hadamard Transform (FWHT) before using chaotic sequences for initial scrambling encryption. Then, the signal is transformed by Discrete Wavelet Transform (DWT) to realize the second round of scrambling and diffusion encryption. This structure increases the security of the encryption algorithm and ensures the efficiency and reliability of the encryption process. The experimental results show that the algorithm has a large key space, good resistance to exhaustive attack, and statistical attack, which can effectively resist chosen plaintext attack. In the decryption process, the algorithm can quickly and accurately decrypt the encrypted speech with good decryption performance. • A speech encryption algorithm based on robust chaos was proposed. • A new 3D-SRCM model is proposed for existing chaotic systems. • The 3D-SRCM model solves chaotic degradation, improving robustness and complexity. • Control parameters were adjusted to adapt to speech signal, linking key and the signal. • In the encryption algorithm, the parameters of the chaotic map are adjusted to fit the speech signal. [ABSTRACT FROM AUTHOR]

The movements of the plankton in the ocean are driven by random diffusion and cognitive judgement with herd-taxis. In this paper, we formulate a phytoplankton–zooplankton model with time delay in the herd-taxis effect diffusion and homogeneous Neumann boundary conditions. The conditions to guarantee the existence of the coexistence equilibrium of the model are given. By analyzing the distribution of the eigenvalues of the characteristic equation, the local asymptotic stability of the coexistence equilibrium is achieved under certain condition. When there is no time delay in the herd-taxis effect, the model can possess the Turing bifurcation when we consider the nonlinear diffusion term, which leads to instability. When taking the time delay into account, the Hopf bifurcation occurs instead as the time delay varies. Furthermore, we investigate the situation without the fact of time, that is the steady-state bifurcation and the stability of bifurcating solution. Finally, the stability of the coexistence equilibrium, the Turing bifurcation and the Hopf bifurcation of the system are modeled by numerical simulation. The simulations shown are coordinated with the theoretical results which we arrive at in the former part of the paper. The results illustrate that the time delay in the herd-taxis effect of the zooplankton influence the dynamics of the plankton system. [ABSTRACT FROM AUTHOR]

Ever since the link between nonlinear science and cryptography became apparent, the problem of applying chaotic dynamics to the construction of cryptographic systems has gained a broad audience and has been the subject of thousands of papers. Yet, the field has not found its place in mainstream cryptography, largely due to persistent weaknesses in the presented systems. The goal of this paper is to help remedy this problem in two ways. The first is by providing a new algorithm that can be used to attack – and hence test the security of – stream ciphers based on the iteration of a chaotic map of the interval. The second is to cast discrete dynamical systems problems in a modern cryptographic and complexity theoretic language, so that researchers working in chaos-based cryptography can begin designing cryptographic protocols that have a better chance of meeting the extreme standards of modern cryptography. [ABSTRACT FROM AUTHOR]

Videos contain temporal information, enabling them to capture the dynamic changes of actions and provide richer visual effects. Traditional video encryption methods involve decomposing videos into frames and encrypting them frame by frame, which results in significant resource consumption. This paper proposes a video encryption method based on temporal action segmentation. This methodology involves the identification and extraction of pivotal frames from a video dataset, followed by the encryption of these significant key frames. This approach serves to enhance the efficacy of the video encryption algorithm. The method consists of three modules. The first module uses temporal action segmentation to classify video frames and extract important frames for the second module's input. The second module encrypts the extracted key frames using a chaos-based encryption algorithm, thereby reducing the time cost of video encryption. The third module outputs the encrypted video. During the encryption process, a large amount of key stream is required. To address this, the paper introduces a new pseudo-random sequence generation method called two-dimensional Gramacy&Lee map (2D-GLM). Comprehensive comparative analysis clearly demonstrates that compared to other systems, 2D-GLM exhibits superior performance and can generate a large number of high-performance pseudo-random sequences. The proposed algorithm is tested on GTEA, and the simulation results demonstrate that it can accomplish video encryption tasks with high security. • Novel 2D-GLM: Outperforms others, ideal for encryption. • Temporal action segmentation boosts video encryption. • Algorithm tested on GTEA dataset, ensuring security. • Efficient video encryption validated with high security. [ABSTRACT FROM AUTHOR]

In this paper, we focus on stochastic delay differential equations in the G-framework (G-SDDEs). We introduce the practical stability to examine whether the performance of G-SDDE near an unstable equilibrium point is acceptable. We establish a new generalized Gronwall inequality based on which we prove the practical mean-square (PMS) exponential stability of G-SDDE. We also establish the stability equivalence between the discrete and the continuous EM approximations for G-SDDE and then show that the continuous EM approximation can preserve the PMS exponential stability of G-SDDE. One numerical experiment is conducted to confirm our theoretical results. • In solving stochastic systems, we usually encounter a probability problem with Knightian uncertainty which can often be characterized by G-Brownian motion. Thus we need to consider the stability and the numerical approximations for the stochastic systems in the G-framework. • In this paper, we have introduced the definitions of practical stability of a dynamical system disturbed by G-Brownian motion (G-SDDE). We have studied the practical mean square (PMS) exponential stability of the G-SDDE under the case that origin is not an equilibrium point by establishing a new generalized Gronwall integral inequality. • We have also introduced the EM method and extended it to a continuous form based on which we have proved that the numerical solution can reproduce the PMS exponential stability of the G-SDDE. [ABSTRACT FROM AUTHOR]

The construction of fractional derivatives with the right properties for use in field theory is reputed to be a difficult task, essentially because of the absence of a unique definition and uniform properties. The conformable fractional derivative introduced in 2014 by Khalil et al. in their seminal paper is a novel and well-behaved definition of fractional derivative for a function that is derivable in the usual sense. In this paper, we investigate the consistency of the Euler–Lagrange formalism for a field theory defined on such a fractional space–time. We especially focus on the relation between symmetries and conservation laws (Noether's currents), about the symmetry group introduced to construct the Lagrangian of the field. In particular, we show that the use of the conformable derivative induces additional terms in the calculation of the action variation. We also investigate the conservation of the Noether current and show that this property only takes place on condition that the equations of motion are verified with a new definition of the conserved law. [ABSTRACT FROM AUTHOR]

Oil palm cultivation stands as a crucial industry in Indonesia, significantly contributing to the nation's economy by generating employment opportunities and fostering social welfare for communities residing near plantations. Despite its economic importance, oil palm plantations face various challenges, with one prominent issue being the infestation of nettle caterpillar pests. These pests cause leaf skeletonization, resulting in a staggering 36% reduction in oil palm productivity over a two-year period. This paper explores diverse strategies for pest management in oil palm plantations, encompassing biological control through the stimulation of natural predators, mechanical control involving the collection and incineration of cocoons, and chemical control through pesticide application. The research introduces a predator–prey mathematical model for oil palm plantation pests, where the leaf area serves as the primary food source for caterpillars, acting as prey. Through dynamic model analysis, four equilibrium points are identified, with interconnected conditions dictating their existence and stability. These conditions are visually represented in a bifurcation plane, providing concise information. The study further includes bifurcation diagrams of equilibrium points to elucidate the influence of each parameter on pests, predators, and the leaf area of oil palm plants. Additionally, sensitivity analysis of the stable interior equilibrium point is conducted to understand the impact of individual parameters. The paper extends its investigation to optimal control strategies, evaluating six scenarios categorized into two population conditions: with predators and without predators. Within each population condition, three control strategies are considered—chemical control only, mechanical control only, and a combination of chemical and mechanical control. Simulation results from the optimal control study reveal that the presence of natural predators emerges as a pivotal strategy in effectively managing nettle caterpillars. Notably, the control of resistant pests through pupa incineration has a substantial impact on reducing the caterpillar population in subsequent life cycles. • In current study, the MELP-S-B predator-prey model is proposed for managing nettle caterpillar pests in oil palm plantations involving the control measures. • The inclusion of prey populations, specifically oil palm leaves, in this predator-prey model constitutes the most fundamental novelty of this study. • The main objective of this research is to determine the dynamics of pests in plantations and avoid economic losses due to pests in oil palm plantations. • In-depth analysis of system dynamics around four equilibrium points conducted. Sensitivity analysis is carried out to measure the influence of parameters at the interior point. • Optimal control study conducted to manage pest abundance in oil palm plantations under varying predator presence. Numerical simulations of six strategies, blending mechanical and chemical measures, offer insights into effective pest control combinations. [ABSTRACT FROM AUTHOR]

Describing the dynamical properties of explored systems, one finds the need to distinguish between various types of trajectories. The nature of trajectories is often split into regular and irregular, which will be shown in this paper as too crude. Hence, the main aim of this paper is to give a classification of trajectories reflecting persistence, regularity, chaos, intermittency, and transiency. To depict such phenomena, classical examples from discrete (the Rulkov map) and continuous (the Lorenz system) dynamical systems are applied. In these cases, the maximal Lyapunov exponent, the 0-1 test for chaos, the bifurcation diagram, and the Fourier analysis are applied, and these dynamics characteristics are confronted with trajectory types. • Trajectory type classification in terms of persistency, regularity, and chaos. • Dynamics characteristics detection tools: bif. diagrams, MLE, the 0-1test for chaos. • Exploration of proposed trajectory classification on discrete and continuous systems. [ABSTRACT FROM AUTHOR]

This paper focus on studying the two-dimensional tabu learning neurons in conjunction with applied currents using phase, bifurcation, eigenvalues and sequence diagrams by semi-analytical method. The result demonstrates that neurons under the influence of different amplitudes can exhibit multi-periodic coexisting attractors. Two special kinds of bifurcation are investigated in depth through the analysis of orbit motions. The accurate tracking of neural spike events through phase diagrams is feasible. This paper also demonstrates the coexistence of steady and unsteady firing patterns, which cannot be obtained by the conventional numerical method. In addition, the correctness of the obtained results is verified by means of field programmable gate array. Lastly, the sequences generated by unsteady motions in the system are combined with DNA image encryption, enhancing the security for image encryption. • The semi-analytical method is used to study the bifurcation tree of a two-dimensional tabu learning neuron systems. • The evolution of supercritical pitchfork bifurcation to subcritical pitchfork bifurcation is investigated. • The coexisting firing behavior of tabu learning neuron is investigated at particular bifurcations. • The initial values of unsteady periodic motions are used as the keys applied to DNA based image encryption. [ABSTRACT FROM AUTHOR]

A study of nonlinear axisymmetric Rayleigh-Bénard magnetoconvection in a cylindrical enclosure filled with a dilute concentration of carbon-based nanotubes in a weakly electrically conducting Newtonian liquid heated from below for various aspect ratios is carried out. Cylindrical geometry is the prototype for heat storage devices and thermal coolant systems with a controlled environment. There is an analogy between porous media and magnetohydrodynamic problems and hence Rayleigh-Bénard magnetoconvection problem is practically important. The solution of the velocity and the temperature is in terms of the Bessel functions of the first kind and hyperbolic functions that are further used to study the marginal stability curves, heat transport, and the dynamical system. Symmetric and asymmetric boundaries of the realistic-type are considered on the horizontal and vertical bounding surfaces. The results of these boundaries are compared with those of the idealistic-type which are symmetric. A unified analysis approach is adopted for all boundary combinations in deriving the Lorenz model and studying the nonlinear dynamics. The time-dependent Nusselt numbers incorporating the effect of the curvature of the cylinder accurately captures the enhanced heat transport situation in the regular convective regime. Further, the influence of various parameters on the indicators of chaos such as the r H -plots, Lorenz attractor, bifurcation diagram, and the time series plot is investigated. The r H -plots clearly point to the appearance of chaos and also assist in determining its intensity and periodicity. The trapping region of the solution of the Lorenz model having the shape like that of a rugby-ball is highlighted in the paper. The size of the ellipsoid shrinks with increase in the strength of the magnetic field and also depends on the boundary conditions. • Axisymmetric convection in shallow cylindrical enclosures is considered. • Investigation is made for symmetric and asymmetric boundary conditions. • Convective instability, heat transports and chaos are studied. • The rH-plots Lorenz attractor, bifurcation diagrams and times-series plots are used to explore the chaotic regime. • Trapping region in the form of a rugby-ball is highlighted in the paper. [ABSTRACT FROM AUTHOR]

In this paper we consider a simple dissipative oscillator, determined by a two-parameter three-dimensional system of ordinary differential equations, obtained from the Nosé–Hoover oscillator by adding a small anti-damping term in its third equation. Based on numerical evidence, complex dynamics of this system was presented in a recent paper, such as the coexistence of periodic orbits, chaotic attractors and a stable invariant torus. Here we analytically prove the existence of a small periodic orbit from which a stable invariant torus bifurcates near the origin of the dissipative oscillator. We also show that the oscillations near the torus present a kind of relaxation oscillation behavior, like canard-type oscillations, commonly found in singularly perturbed systems. The obtained results extend and provide analytical proofs for some dynamical properties of the considered system, which were numerically described in the literature. [Display omitted] • A dissipative oscillator, based on Nosé–Hoover with a small term, is studied. • Analytical proof of small orbit and stable torus existence near origin. • Near-torus oscillations with canard-like behavior, as in singularly perturbed systems. [ABSTRACT FROM AUTHOR]

High-dimensional chaotic maps offer a larger parameter space, increased complexity, and enhanced resilience against dynamical degradation compared to their one-dimensional counterparts. Therefore, they are gradually replacing one-dimensional chaotic maps in various applications. However, many methods for generating high-dimensional chaotic maps lack mathematical proofs, which cannot theoretically ensure their chaotic nature. Even high-dimensional chaotic maps with theoretical support often lack global transitivity and exhibit local chaos. Applying such chaotic maps in chaos-based stream ciphers or random number generators results in poor randomness of generated chaotic sequences, reduced internal state space, and numerous weak keys, which is not ideal. This paper proposes a systematic method for constructing high-dimensional chaotic maps (called dispersal maps). The paper proves that the maps constructed are topologically mixing across the entire space and are hyper-chaotic on an invariant subset of full measure. These properties make them satisfy almost all definitions of chaos, and their chaotic dynamical behavior is global: exhibiting transitivity across the entire phase space rather than a local subregion, a dense scrambled subset rather than a tiny one, and being hyper-chaotic almost everywhere rather than on a local attractor. Therefore, dispersal maps can improve the existing problems of locally chaotic maps in application. The experiments also indicate that dispersal maps exhibit ergodicity on the phase space, with highly uniform trajectory distributions and sensitivity to initial perturbations. The findings provide researchers with ideal chaotic maps and a feasible method for constructing high-dimensional chaotic maps with global chaos. • Offer a general method for constructing chaotic maps with any dimension • Ensure the chaos of the constructed maps through rigorous theory • The maps are topologically mixing, resulting in global transitivity and chaos in multiple senses. • Introduce the concept of diffusion maps to provide a new idea to prove the chaos of maps [ABSTRACT FROM AUTHOR]

The implications of neural synchronization extend beyond brain function, and can impact the development of artificial neural networks. This paper explores the synchronization of multiple fractional-order fuzzy complex-valued spatiotemporal neural networks (MFOFCVSNNs), which is novel and characterized using fuzzy logic and fractional-order partial differential equations, making it more adaptable and versatile. We first establish a new fractional-order complex-valued partial differential inequality, an integer-order complex-valued partial differential inequality, and an equation. Then, by combining the Lyapunov method with fuzzy set theory, employing newly established inequalities and equations, along with a newly designed fuzzy pinning controller, we derive two linear matrix inequality (LMI) formulations of synchronization criteria for MFOFCVSNNs using a direct non-complex decomposition approach. These criteria exhibit different dependencies on the membership function, with one being independent and the other dependent. Importantly, the criterion based on the membership function demonstrates reduced conservatism compared to its independent counterpart. By leveraging M -matrix theory, we present the synchronization criteria in a concise low-dimensional form. Moreover, this paper extends and enhances previous findings, resulting in reduced conservatism. Finally, we validate our theoretical analysis through numerical simulations. • A new model is proposed-multiple fractional-order fuzzy complex-valued spatiotemporal neural networks, which is novel and characterized using fuzzy logic and fractional-order partial differential equations, making it more adaptable and versatile. • Proposing a novel fuzzy pinning controller for large-scale networks, it streamlines implementation complexity and enhances design flexibility by not requiring identical fuzzy parameters as the model. • Exploring synchronization among multiple fractional-order fuzzy complex-valued delayed spatiotemporal neural networks without utilizing the complex-valued decomposition method. • The membership-function-independent synchronization criterion and the membership-function-dependent synchronization criterion are established. [ABSTRACT FROM AUTHOR]

In this paper, we derive new results on the averaging principle for a class of Caputo neutral stochastic system driven by Markovian switching and Lévy noise with variable delays and time-varying fractional order. Under a set of appropriate conditions, we showed that solutions of the averaged stochastic systems approach the solutions of the original stochastic systems in the sense of both convergences in mean square and convergence in probability. Finally, we attach two examples with numerical simulations to justify the validity of our theory. • Our paper presents a general class of variable-order Caputo neutral differential equations. • We investigate the averaging principle under a new set of suitable assumptions. • Averaging result is proved in both senses, convergence in mean square and convergence in probability. • We provide some numerical simulations to illustrate the validity of our results. • Our findings improve and extend some related conclusions on the topic of averaging principle. [ABSTRACT FROM AUTHOR]

A new fractional-order 5D hyperchaotic system based on memristor is constructed in this paper, with the speciality that the system exists chaotic and hyperchaotic states in the fractional-order case, while in periodic state in the integer-order. In addition, it has a variety of special phenomena at fractional-order such as infinite initial value range, parameter-dependent offset-boosting and amplitude control, attractor coexistence, and fractional order complexity greater than integer order. The correctness and feasibility of the system is verified by analog circuit simulation and hardware circuit implementation. Combining this system with image encryption algorithms, two new scrambling algorithms and a diffusion algorithm are proposed. And a high-quality encryption scheme that can be applied to a wide range of color images is proposed. The scheme is found to have excellent security after verification by various security analyses and comparison with other literatures. This paper provides a basis for the superiority of fractional-order chaotic systems and provides new methods in the field of image encryption. • We construct a fractional-order 5D hyperchaotic system based on memristor. • The system is chaotic only to fractional-order and has a rich and complex dynamical behavior. • We propose a possible mechanism for the generation of attractor coexistence. • Designed new encryption algorithms and proposed a new color image encryption scheme [ABSTRACT FROM AUTHOR]

Several graph models are available today to model online social networks. These graph models are used to analyze the structural properties of the online social network, such as detecting communities, finding the influential spreader and predicting the behavior of the network. However, these models are based on deterministic single-layer graphs that may not be appropriate when online users use multiple social networks at the same time and social networks provide specific services. Moreover, because of the unknown and dynamic nature related to the behaviors and activities of online users, as well as structural and behavioral parameters, which may vary over time, stochastic multi-layer models could be applied to better capture and represent this phenomenon, as well as the dynamic nature of social networks. For example, in recommender systems, users' interests are unknown parameters and vary over time. Therefore, stochastic multilayer graph modeling can be used to develop recommender systems by considering different layers for different types of interests or preferences. In this paper, we propose a stochastic multilayer graph in which the edges are associated with random variables as a potential graph model for the analysis of online social networks. Therefore, after redefine some network measures related to stochastic multilayer graphs, we propose a Cellular Goore Game (CGG) based algorithm to computes the redefine network measures. A CGG-based algorithm computes defined network measures by learning automata from the edges of stochastic multilayer graphs. The experimental results show that the new CGG-based algorithm requires fewer samples from the edges of stochastic multilayer graphs than the standard sampling method in network measures calculation. Furthermore, the obtained results demonstrate that, from an evaluation perspective, the CGG-based algorithm provides superior results in terms of Kolmogorov-Smirnov (KS-test), Pearson Correlation Coefficient (PCC), Normalized Root Mean Square Error (NRMSE) and Kullback–Leibler divergence (KL-test). • The paper opens up a new horizon by introducing stochastic multilayer graphs as a model for real social networks. • This paper defines some new network measures for stochastic multilayer graphs. • We present a novel algorithm for estimating stochastic multilayer graph measurements based on the Cellular Goore Game (CGG). • The algorithm works via distributed computing to estimate stochastic multilayer graph measurements with learning automata. • The simulation results show that the proposed model outperforms a similar model in modeling real-world multilayer graphs. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior in a spatially heterogeneous reaction–diffusion SIS epidemic model with general nonlinear incidence and Dirichlet boundary condition is investigated. The well-posedness of solutions, including the global existence, nonnegativity, ultimate boundedness, as well as the existence of compact global attractor, are first established, then the basic reproduction number R 0 is calculated by defining the next generation operator. Secondly, the threshold dynamics of the model with respect to R 0 are studied. That is, when R 0 < 1 the disease-free steady state is globally asymptotically stable, and when R 0 > 1 the model is uniformly persistent and admits one positive steady state, and under some additional conditions the uniqueness of positive steady state is obtained. Furthermore, some interesting properties of R 0 are established, including the calculating formula of R 0 , the asymptotic profiles of R 0 with respect to diffusion rate d I , and the monotonicity of R 0 with diffusion rate d I and domain Ω. In addition, the bang–bang-type configuration optimization of R 0 also is obtained. This rare result in diffusive equation reveals that we can control disease diffusion at least at one peak. Finally, the numerical examples and simulations are carried out to illustrate the rationality of open problems proposed in this paper, and explore the influence of spatial heterogeneous environment on the disease spread and make a comparison on dynamics between Dirichlet boundary condition and Neumann boundary condition. [ABSTRACT FROM AUTHOR]

For uncertain fractional-order nonlinear systems (UFONS) with unknown control coefficients and intermittent actuator faults, the asymptotic tracking control problem is investigated in this paper. Firstly, to weaken the influence of virtual control coefficients and intermittent actuator faults, a smooth fractional-order projection operator-based adaptive compensation mechanism is presented. Additionally, a fractional-order nonlinear filter is constructed to replace the fractional-order derivative of virtual control functions approximately, which not only avoids the issue of complexity explosion existed in backstepping control frame, but fully compensates the effects of boundary errors caused by the employed filter in spite of the unknown virtual control coefficient. By constructing a fractional Lyapunov function from the property of projection operator, it is proved that all signals in the closed-loop system are bounded, and the asymptotic tracking control object is achieved. Definitively, a simulation study is presented to verify the availability of the presented method. • This paper investigates the issue of asymptotic tracking control design for fractional-order nonlinear systems with unknown control coefficients and actuator faults. • Firstly, in order to weaken the influence of virtual control coefficient, an adaptive compensation mechanism based on the smooth fractional-order projection operator design method is proposed. • Additionally, a fractional-order nonlinear filter is constructed to approximately replace the virtual control functions as well as its fractional-order derivative, which not only avoids the inherent complexity explosion problem under the framework of backstepping, but also fully compensates the effect of boundary error caused by the introduced filter when the virtual control coefficient is unknown. [ABSTRACT FROM AUTHOR]

The research on cascading failures in static networks has become relatively mature, and an increasing number of scholars have started to explore the network scenarios where mobile nodes and static nodes coexist. In order to enhance the resilience of static-mobile networks against cascading failures, an algorithm based on Q-learning for optimizing the path of the mobile node is proposed in this paper. This paper proposes a Q-learning-based algorithm for optimizing the path of the mobile node. To achieve this objective, a cascading failure model is established based on sequential interactions between mobile nodes and static nodes in this study. In this model, the motion paths of the mobile node are generated by the Q-learning algorithm. Based on this approach, extensive experiments are conducted, and the results demonstrate the following findings: 1) By increasing the adjustable load parameters of static nodes in the network, the occurrence of cascading failures is delayed, and the frequency of cascading failures is decreased. 2) Increasing the adjustable load parameter, capacity parameter, and network size of static nodes contributes to the network's resilience against cascading failures. 3) As the communication radius of the mobile node increases, the scale of failures in the static network initially increases and then decreases. 4) Different trajectories of the mobile node have a significant impact on network robustness, and paths generated based on Q-learning algorithm exhibit significantly improved network robustness compared to Gaussian-Markov mobility trajectories. The Q-learning algorithm is compared to the Ant Colony Optimization algorithm in terms of execution time, path length, and network robustness, and the Q-learning algorithm demonstrating favorable performance. These experimental results can be valuable for theoretical research on cascading failures in static-mobile networks. • A novel methodology is proposed to optimize the path of the mobile node, effectively enhancing the network's resilience against cascading failures. • The motion trajectories of the mobile node are generated using a Q-learning-based algorithm. • The paths generated based on the Q-learning algorithm exhibit significantly improved network robustness compared to Gaussian-Markov mobility trajectories. • As the communication radius of the mobile node increases, the scale of failures in the static network initially increases and then decreases. [ABSTRACT FROM AUTHOR]

Numerous studies have explored the relationship between cooperation and inter-individual trust. However, the understanding of the dynamic interaction process of trust among networked agents with bounded rationality remains limited. To bridge this gap, this paper develops an evolutionary game model that incorporates a trust perspective considering emotional scaling. Trust is quantified based on individuals' limited memory of interaction experiences, acting as a perturbation factor that influences cooperative strategies. The role of emotional factors, particularly guilt and anger, in trust formation is emphasized. Extensive numerical simulations reveal that introducing trust greatly enhances cooperation in the system, especially in networks with lower randomness. Trust-based cooperative decision-making demonstrates evident historical path dependence characteristics. Notably, the effects of emotions differ. Guilt effectively motivates defectors to switch strategies, thereby enhancing cooperation. In contrast, the influence of anger on cooperation diminishes as it becomes intertwined with other factors during the trust-building process. The empirical results of higher returns for low-trust groups have also been validated in this paper. Overall, this work contributes to a deeper understanding of the mechanisms underlying cooperation formation. • A trust-based evolutionary game model with emotional scaling is developed. • The emphasis is on the interaction between network structure and emotions. • Trust-based cooperation exhibits clear historical path dependence. • Guilt and anger emotions have distinct impacts on the emergence of cooperation. [ABSTRACT FROM AUTHOR]

Introducing memristors into the traditional chaotic system can generate multiscroll chaotic attractors, expanding possibilities for information processing and chaotic applications. This paper first proposes a novel multi-segment memristor model based on a multi-segment linear function. Then, based on the Sprott-B system, one-directional memristive multiscroll chaotic attractors (1D-MMSCAs), 2D-MMSCAs, and 3D-MMSCAs are produced separately, with different numbers of novel memristors introduced. The dynamic behavior of the MMSCAs is analyzed in terms of equilibrium points, Lyapunov exponents and bifurcations, coexisting attractors, and complexity. Lyapunov exponent and bifurcation analysis reveal rich dynamic behavior of the MMSCAs, including period-doubling bifurcations, bursts of chaos, and transient of chaos. The MMSCAs exhibit dynamic phenomena such as coexisting attractors, multistability, and super multistability under different initial conditions. Furthermore, the existence and feasibility of the MMSCAs are verified through circuit simulation. Coexisting attractors generation circuits that can change the initial values of arbitrary state variables are designed. Using an improved Euler algorithm and the STM32 microcontroller, the MMSCAs are digitally implemented, expanding the application scope. Comparative results with other multi-scroll chaotic attractors (MSCAs) demonstrate the advantages of the proposed MMSCAs, including controllable scroll number and direction, simple implementation circuits, and rich dynamic behavior. Finally, the MMSCAs are applied to finite-time synchronization. Simulation results show that the two proposed synchronization schemes in this paper require less time to achieve complete synchronization compared to other synchronization schemes. This characteristic enhances the efficiency and practicality of the proposed synchronization strategy in real-world applications. [ABSTRACT FROM AUTHOR]

Stefan melting problems involve the tracking of a sharp melt front during the heat conduction controlled melting of a solid. A feature of this problem is a jump discontinuity in the heat flux across the melt interface. Time fractional versions of this problem introduce fractional time derivatives into the governing equations. Starting from an appropriate thermodynamic balance statement, this paper develops a new sharp interface time fractional Stefan melting problem, the memory-enthalpy formulation. A mathematical analysis reveals that this formulation exhibits a natural regularization in that, unlike the classic Stefan problem, the flux is continuous across the melt interface. It is also shown how the memory-enthalpy formulation, along with previously reported time fractional Stefan problems based on a memory-flux, can be derived by starting from a generic continuity equation and melt front condition. The paper closes by mathematically proving that the memory-enthalpy fractional Stefan formulation is equivalent to the previous memory-flux formulations. A result that provides a thermodynamic consistent basis for a widely used and investigated class of time fractional (memory) Stefan problems. • A new time fractional Stefan problem is presented, the memory-enthalpy formulation. • The problem is obtained from an appropriate thermodynamic balance statement. • We prove that this formulation exhibits a natural regularization of the problem. • A comparison with the previous memory-flux formulation is made. • We prove that the memory-enthalpy formulation is equivalent to the memory-flux one. [ABSTRACT FROM AUTHOR]

The paper presents a study of issues related to the identification of a non-linear mathematical model describing dynamics of the temporomandibular joint (TMJ) disc. Based on the tests of real disks, a non-linear model was built and verified, and then numerical simulations were carried out, the purpose of which was to analyze the behavior of the model for various excitation conditions. They include, among others, plotting a multi-colored map of distribution of the largest Lyapunov exponent based on which the areas of occurrence of periodic and chaotic motion zones are identified. Bifurcation diagrams of steady states for sample sections of the Lyapunov map and phase flows of periodic and chaotic solutions are generated. For the same sections, numerical simulations are performed to identify coexisting solutions. These studies are carried out using diagrams showing the number of coexisting solutions and their periodicity. The research presented in the paper shows a very good match between the results of computer simulations and the data recorded in the laboratory experiment. Due to the very strong damping occurring in the system, the chaotic attractors resemble quasi-periodic solutions with their geometric shape. Strong damping also significantly affects multiple solutions, which are relatively rare in the analyzed model. Most of the chaotic responses and multiple solutions occur in the range of low amplitude values of the dynamic load affecting the tissues of the articular disc. The obtained results of numerical experiments clearly indicate that in the range of low frequency values of the external load acting on the system, single periodic solutions with a periodicity of 1 T dominate. With the increase of the load amplitude, the area of occurrence of such solutions increases. [Display omitted] • A novel non-linear mathematical model of the TMJ disk has been proposed. • The model was very well adjusted to the results of experimental studies. • The behavior of the model for chaotic and periodic motion zones was tested. • The presence of coexisting solutions was confirmed. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for solving fractional delay differential equations of variable order using the spectral element method. The proposed method overcomes the limitations of traditional spectral methods, such as poor approximation in long intervals and inefficiency in high degrees. By introducing a variable order differentiation matrix and using basic Lagrangian functions to approximate the solution in each element, the method achieves high accuracy and efficiency. A penalty method is also applied to minimize the jump of fluxes at interface points, and the effectiveness of this approach is analyzed. Finally, three benchmark problems are solved, and the convergence analysis demonstrates the effectiveness and efficiency of the proposed method. In essence, this paper offers a significant contribution to the literature on fractional differential equations and their numerical solution methodologies. • New approach for solving fractional delay differential equations using spectral element method. Overcomes limitations of traditional methods. • Introduces variable order differentiation matrix and Lagrangian functions for high accuracy. Penalty method minimizes flux jumps at interface points. • Rigorous convergence analysis of proposed method. • Effectiveness demonstrated with practical examples and discretization. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive security analysis on an improved chaos-based image encryption algorithm. The initial algorithm, proposed by Li et al., involves permutation related to the sum of plaintext pixel values and diffusion associated with 9 specific pixel values in the permuted image. However, a thorough analysis conducted by Liu et al. reveals two major flaws in it: firstly, the 9 specific pixel values are not involved in the diffusion process; secondly, the permutation method exhibits significant vulnerabilities. In response to these shortcomings, Liu et al. proposed targeted improvements on it, which include incorporating a permutation step for the 9 specific pixels and enhancing the original permutation method. In this study, we analyze the improved algorithm and discover that it still possesses security vulnerabilities, rendering it susceptible to chosen-plaintext attack. By constructing three categories of special plaintexts, one can decipher the equivalent permutation and diffusion. Theoretical analysis and experimental results provide strong evidence for the effectiveness of our analysis in this paper. [ABSTRACT FROM AUTHOR]

A close relation has recently emerged between two of the most fundamental concepts in physics and mathematics: chaos and supersymmetry. In striking contrast to the semantics of the word 'chaos', the true physical essence of this phenomenon now appears to be a spontaneous order associated with the breakdown of the topological supersymmetry (TS) hidden in all stochastic (partial) differential equations, i.e. , in all systems from a broad domain ranging from cosmology to nanoscience. Among the low-hanging fruits of this new perspective, which can be called the supersymmetric theory of stochastic dynamics (STS), are theoretical explanations of 1/f noise and self-organized criticality. Central to STS is the physical meaning of TS breaking order parameter (OP). In this paper, we discuss that the OP is a field-theoretic embodiment of the 'butterfly effect' (BE) – the infinitely long dynamical memory that is definitive of chaos. We stress that the formulation of the corresponding effective theory for the OP would mark the inception of the first consistent physical theory of the BE. Such a theory, potentially a valuable tool in solving chaos-related problems, would parallel the well-established and successful field theoretic descriptions of superconductivity, ferromagnetism and other known orders arising from the spontaneous breakdown of various symmetries of nature. • The paper provides a concise review of a theory that reveals that dynamical chaos is a spontaneous order. • It is shown that the corresponding order parameter describes the butterfly effect. • It is discussed how this theory lays the foundation for the first consistent physical theory of the butterfly effect. • It is argued that in some cases, the butterfly effect may admit a holographic field-theoretic description. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and develop two novel classifications of enriched (q , θ) -contractions on Banach spaces. The paper includes illustrative examples to demonstrate these concepts and establishes the convergence of Krasnoselskii's iteration method when applied to approximate the fixed point of such enriched (q , θ) -contractions. Additionally, the paper explores the application of these concepts in constructing the fractals of the corresponding Hutchinson–Barnsley operators. The above construction is illustrated by some examples. These discoveries provide new fixed-point solutions for iterated function systems under various contractive conditions. Finally, as an application of our main result, the existence of the solution to the problem of fourth order differential equation is presented. Furthermore, the findings not only validate but also enhance and expand upon multiple established conclusions in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate soliton solutions for the nonlocal Kundu-nonlinear Schrödinger (Kundu-NLS) equation by the inverse scattering transform. The inverse scattering transform and scattering data are studied through a symmetry reduction r (x , t) = q ∗ (− x , t). Then we can derive the exact solutions by Gelfand–Levitan–Marchenko (GLM) equation. Specially, the one-soliton, two-soliton solutions and corresponding graphs of the nonlocal Kundu-NLS equation are given. • The main purpose is to get the exact solutions for the nonlocal Kundu-NLS equation by the scattering data and GLM equation. • This paper is the extension and application of the inverse scattering transform in nonlocal equations. • The inverse scattering transform can be used to solve more nonlocal equations in the future. [ABSTRACT FROM AUTHOR]

In this paper, we consider the replicator-mutator dynamics for pairwise social dilemmas where the payoff entries are random variables. The randomness is incorporated to take into account the uncertainty, which is inevitable in practical applications and may arise from different sources such as lack of data for measuring the outcomes, noisy and rapidly changing environments, as well as unavoidable human estimate errors. We analytically and numerically compute the probability that the replicator-mutator dynamics has a given number of equilibria for four classes of pairwise social dilemmas (Prisoner's Dilemma, Snow-Drift Game, Stag-Hunt Game and Harmony Game). As a result, we characterise the qualitative behaviour of such probabilities as a function of the mutation rate. Our results clearly show the influence of the mutation rate and the uncertainty in the payoff matrix definition on the number of equilibria in these games. Overall, our analysis has provided novel theoretical contributions to the understanding of the impact of uncertainty on the behavioural diversity in a complex dynamical system. • The paper analyses replicator-mutator dynamics for pairwise social dilemmas where the payoff entries are random variables. • We analytically and numerically compute the probability that the replicator-mutator dynamics has a given number of equilibria. • We study four pairwise social dilemmas, Prisoner's Dilemma, Snow-Drift Game, Stag-Hunt Game and Harmony Game. • We characterise the qualitative behaviour of such probabilities as a function of the mutation rate. • Our results show strong influence of the mutation rate and payoff randomness on the number of equilibria. [ABSTRACT FROM AUTHOR]

In this paper, we study the synchronization of complex-valued stochastic complex networks (SCNs) with unbounded time delays via unbounded impulsive control under cyber attacks. This paper considers unbounded delays for the first time in complex networks. By the combination of Lyapunov–Razumikhin method and graph theory, several criteria for realizing p th moment exponential synchronization (PMES) can be obtained, which are associated with the intensity of impulsive control, unbounded time delays and cyber attacks. In the end, we search the PMES of a class of complex-valued stochastic coupled Chua's circuit systems under network attacks to validate the reliability and effectiveness of the results. • This paper considers unbounded delays for the first time in complex networks. • The delayed impulsive controls used in this article is allowed to be unbounded. • We introduce the delayed impulsive controller that is subject to deception attacks. • This paper deals with system states that is complex-valued. • In this paper, we relax the condition that it is not required that the derivative of the Lyapunov function is not always less than 0. [ABSTRACT FROM AUTHOR]

Due to the maturation of research on chaos and secure communication, the control technology of nonlinear systems, specifically chaos synchronization, has captured the attention of numerous researchers. Focusing on the issues of inflexibility in the design of chaotic synchronization controllers, the need for prior synchronization of the target system structure, and noise's disruptive impact on synchronization, this paper presents solutions that enhance the practical application of chaos. Firstly, the RBF neural controller is adjusted in this paper to bolster the control precision of the chaotic system and enhance its resilience to external disturbances. Secondly, this article presents an enhanced PSO optimization algorithm for the improved RBF neural controller to improve the optimization efficiency of the controller parameters. Finally, the simulation results of the Lorenz system validate the feasibility of the proposed synchronization control scheme. Additionally, the use of chaotic synchronization in image encryption demonstrates that synchronization accuracy can fulfill the requirements of image encryption application scenarios. • The structure of the RBF neural controller is improved to achieve better synchronization control performance, including synchronization accuracy and noise resistance. • The PSO algorithm is improved specifically for the intelligent chaotic controller studied in this article to enhance the efficiency of searching for RBF controller parameters. • Reduce the number of controllers used for synchronizing, improve the robustness of the synchronization system to noise, and a flexible and straightforward chaotic synchronization controller design. [ABSTRACT FROM AUTHOR]

At present, taxi market is in a transition phase, with traditional vehicles coexisting with driverless vehicles, and online services going side-by-side with offline services. In view of this, this paper put forward an evolutionary game model of tripartite competition involving passengers, driverless taxis, and traditional taxis, whereby the influence of factors, such as the scale and fare of driverless taxis, on the stable equilibrium state of the dynamical system is studied. Simulation results show that game players are very sensitive to the change of cost in terms of strategy choice: within the range of feasible parameters, the system converges to a stable state where passengers, driverless taxis, and traditional taxis all adopt online services, or all adopt offline services, depending on the ratio of driverless taxi fare to traditional taxi fare. Besides, the scale of driverless taxis and the corresponding technological level also exert an impact on the evolution of system dynamics: reducing the cruise energy consumption of driverless vehicles or improving the scheduling level of the platform can significantly promote taxi online service modes. Through this simple but representative model, the paper provides a new research idea and framework for the development of driverless taxi service modes. • An evolutionary game model is proposed to investigate taxi mode selection. • The game system is most sensitive to the change in driverless taxi fares. • The option of low-price strategy plays a role as a "double-edged sword". • Improving technological level of driverless taxi facilitates online service modes. [ABSTRACT FROM AUTHOR]

In order to solve the problems of nonlinearity, strong coupling and fractional order characteristics of multiple physical and chemical processes in the proton exchange membrane fuel cell (PEMFC) system modeling process, this paper proposes a multiple-input multiple-output (MIMO) fractional-order Hammerstein model with colored noise based on a data-driven method to describe the PEMFC system. First, in order to reduce the modeling complexity and improve the calculation efficiency, the canonical correlation analysis (CCA) and the correlation analysis (CA) are combined to select the controllable variables with the greatest correlation with the system output as the model input variables; Secondly, the fractional order theory is combined with the Hammerstein model, and the MIMO fractional order Hammerstein model with colored noise is derived by taking into account the complexity of the actual noise of the PEMFC system; Then, on this basis, it is proposed to combine the multi-innovation identification principle with the Levenberg–Marquardt algorithm, make full use of current data and historical data to improve the identification accuracy, and thereby estimate the unknown parameters of the system and the fractional order of the system. Finally, experiments based on actual data verified the accuracy and effectiveness of the proposed modeling method and identification algorithm. The method proposed in this paper can significantly improve the identification accuracy, and the established identification model of the PEMFC system can accurately describe its true dynamic process. • Combining CCA and CA to screen out the input variables that have a greater impact on the electrical quality of the PEMFC. • The MIMO fractional-order Hammerstein model with colored noise of the PEMFC system is derived. • The proposed multi-innovation identification algorithm improves identification efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Identifying critical nodes in complex networks is a fundamental problem, it plays a crucial role in stabilizing the performance of the network structure and propagating information. Majority of the existing studies are built by directly considering the topology of the network. In this paper, a new vertex centrality called distance Laplacian centrality (DLC) is proposed for critical nodes identification from the perspective of graph energy. This method incorporates the vertex's transfer degree, considers the position of nodes in the network from a global perspective, and measures the importance of a node using the relative variation of the distance Laplacian energy responding to the deletion of the node from the network. To validate the performance and applicability of the proposed method, this paper compares DLC with other methods through susceptible-infected-recovered (SIR) model on different real networks. The experimental results demonstrate that DLC has better performance in terms of influence, distinguishing ability relevance and ranking accuracy, and can effectively recognize critical nodes in complex networks. • A novel method is proposed to identify the critical nodes in the network. • The proposed method is presented from the perspective of the distance Laplacian energy. • The new method incorporates the transfer degree of nodes, which more accurately reflects the topology of the network. • The proposed method has better performance in terms of the influence, distinguishing ability, relevance and ranking accuracy. [ABSTRACT FROM AUTHOR]

This paper introduces a novel and complex Unsaturated Piecewise Linear Quad-Stable Stochastic Resonance System (UPLQSR) to address the issue of output saturation in the Classical Quad-Stable Stochastic Resonance (CQSR) system. By linearizing the structure of the potential function, the constraints imposed by high-order terms are effectively eliminated, allowing Brownian particles to move more freely. Numerical simulations demonstrate that UPLQSR achieves significantly higher output signal amplitudes compared to CQSR, highlighting its remarkable signal amplification capability. By analyzing the structure of the potential function, the relationship between the height of the potential barrier and the aggressiveness of the particles jumping is determined. Utilizing adiabatic approximation theory, the paper derives the Steady-state Probability Density (SPD), Mean First Passage Time (MFPT), and Spectral Amplification (SA), revealing the specific process of the particle jumping, as well as the influence of the parameters on the performance of the UPLQSR. After optimizing parameters using the Adaptive Genetic Algorithm (GA), UPLQSR is applied to the early fault diagnosis of various bearing models under Gaussian white noise, demonstrating superior fault detection capabilities. In summary, this study pioneered the theory of non-saturation of quad-stable systems, optimized the weak signal detection technique, and provided a more accurate means of signal identification and analysis, highlighting its great value of application in engineering. [ABSTRACT FROM AUTHOR]

The Chialvo hyperneuron model is introduced as the extension of the scalar Chialvo neuron model in this paper. The complexity of the model is increased not by adding another spatial variable but by replacing scalar nodal variables with square matrices of iterative variables. It is shown that such an extension does yield the effect of the divergence if the matrices of iterative variables are nilpotent matrices and the Lyapunov exponent of the scalar Chialvo neuron model is positive. Different regimes of divergence are classified into the finite-time and the explosive divergence of the hyperneuron. Analytical and computational simulations are used to illustrate the complex dynamical behavior of the Chialvo hyperneuron not observable in the scalar Chialvo neuron model. • The Chialvo hyperneuron model is presented in this paper. • Scalar nodal variables in the Chialvo neuron model are replaced by square matrices. • Analytical relations of the proposed Chialvo model are derived in the explicit form. • Conditions for the finite-time divergence of the Chialvo hyperneuron model are determined. [ABSTRACT FROM AUTHOR]

Pine wilt disease is one of the most serious forest pest and disease in China, which seriously influences the realization of the dual carbon goal. In this paper, considering susceptible longhorns and infected longhorns, we study a delayed reaction–diffusion pine wilt disease model both with memory diffusion and nonlocal effect. We analyze the dynamic properties for with and without memory diffusion and nonlocal effect, respectively. Especially, for this model, we find that memory diffusion plays a leading role in spatial dynamics. Memory diffusion can induce spatially inhomogeneous periodic solutions and steady-state solutions. Nonlocal effect mainly affects the amplitude and period of spatially inhomogeneous periodic solutions of the system. In addition, we give some biological explanations for the different phenomena in this paper. • Diffusive PWD model with memory diffusion and nonlocal effect is proposed. • Dynamics of the system with and without memory diffusion and nonlocal effect are compared. • Memory diffusion can induce spatially inhomogeneous periodic and steady-state solutions. • Nonlocal effect has impact on the amplitude and period of spatially inhomogeneous periodic solutions. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of network security for stealthy false data injection (FDI) attacks under modified Kalman filtering (MKF) over complex networks with non-Gaussian-Lévy noise (NGLN). Initially, a modified Kalman filter (MKFR) is proposed to estimate system states, where the estimation function is related to the probabilistic characteristics of Lévy noise, and the saturation threshold is designed in relation to Lévy noise parameters. The upper bound of error covariance is obtained, and the boundedness of the upper bound is proven through the use of mathematical induction and iterative methods. Second, based on the MKF, this paper proposes a two-channel stealthy FDI attacks (TSFAs) strategy that is related only to the system model, which is injected into the sensor-to-controller (S-C) and controller-to-actuator (C-A) transmission channels at the same time. In addition, the attacker sets two MKFRs as observers to estimate the states of the target system, which are used to adjust the attack signal. Third, a sufficient condition is obtained that demonstrates the stability of the system. Meanwhile, TSFAs can avoid being detected by the residual-based detector to guarantee stealthiness. Finally, the effectiveness of the MKF is verified by the numerical simulation, and the stealthiness of the TSFAs and the impact on the system stability are also demonstrated. • Non-Gaussian-Lévy noise where both the process noise and the measurement noise have unknown covariance is studied. • The modified Kalman filtering method is proposed which is related to the probabilistic characteristics of Lévy noise. • By utilizing the mathematical induction and the iterative method, the boundedness of error covariance is proved. • The two-channel stealthy FDI attacks model is related only to the system model and can bypass the residual-based attack detector. [ABSTRACT FROM AUTHOR]

The memory fractional effects of a one-axis twisting model on the dynamics of two-qubit entanglement and non-locality are discussed. It consists of solving the time-dependent fractional Schrödinger equation by extending any integration into non-integer orders using Riemann–Liouville integration. The obtained results present the possibility of controlling the fractional order of memory, varying the parameters to significantly generate concurrency and Bell's non-locality. Under the current investigation setup, it is noticeable that the behaviors of the proposed quantifiers are similar to each other, but with a small difference in the amplitude of non-locality with respect to entanglement. Importantly, we show that the most intriguing aspect of this paper is to detect that pair-qubit entanglement and non-locality can be preserved for an indefinite time, which still holds significance in quantum information processing. • In this paper a model based on the interaction between two-qubit system by using twisting model. • We solved the fractional Schrödinger equation. • We studied concurrence, Bell non-locality and coherence. [ABSTRACT FROM AUTHOR]

This paper presents a novel memristive synapse-coupled ring neural network (MSCRNN) through introducing a nonvolatile memristor into a three-neuron Hopfield neural network connected by a unidirectional ring topology. Complex dynamics relying on control parameters and initial states is thoroughly explored using numerical analysis techniques. Numerical analyses show that the MSCRNN not only exhibits bistability, tristability, but also in particular evolves an intriguing phenomenon known as homogeneous multistability, characterized by the emergence of an infinite number of homogeneous coexisting attractors triggered by the memristor initial states. In addition, a hardware test platform based on the CH32 microcontroller is built to experimentally validate these numerical findings. Finally, a new pseudorandom number generator is developed taking advantage of memristor initial-regulated chaotic sequences derived from the MSCRNN. Performance analysis outcomes indicate that these chaotic sequences possess the capability to generate pseudorandom numbers demonstrating exceptional randomness, rendering them highly advantageous for utilization in various chaos-based engineering applications. • A new memristor model is used to emulate synaptic plasticity among the ring neural network. • The MSCRNN exhibits an infinite number of homogeneous coexisting attractors. • A pseudorandom number generator is developed utilizing the chaotic sequences. [ABSTRACT FROM AUTHOR]

Persistence of solitary wave solutions of the regularized long wave equation with small perturbations are investigated by the geometric singular perturbation theory and bifurcation theory. Two different kinds of the perturbations are considered in this paper: one is the Kuramoto–Sivashinsky perturbation, the other is the Marangoni effects. Indeed, the solitary wave persists under small perturbations. Furthermore, the different perturbations do affect the proper wave speed c ensuring the persistence of the solitary waves. Finally, numerical simulations are utilized to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

Dynamical rewiring widely exists in complex systems, however the impact of dynamical rewiring in the synchronization of neural systems is currently unknown. In this paper, we use memristive FitzHugh-Nagumo neurons to construct random, small-world and scale-free networks in which the connections between neurons can be rewired, and investigate the influence of rewiring on the synchronization of neural networks in with/without Gaussian white noise, and comparing it to the corresponding static networks. We found that dynamical rewiring enhances the synchronization of the network, and the degree of synchronization will be higher when the rewiring period is shorter and the rewiring proportion is larger. In addition, the synchronization of the network gradually diminishes as the coupling strength decreases and the noise intensity increases, and rewiring networks always exhibit superior synchronization to static networks since the dynamical rewiring enhances the interaction between neurons. Our study shows that neural network models with dynamically changing topology are more suitable and realistic network models, which may reveal the profound significance of dynamic rewiring for the multifaceted dynamic flexibility and adaptability of neural systems. • Memristive FitzHugh-Nagumo model is employed to construct random, small-world and scale-free networks. • Dynamical rewiring of connections between nodes is considered into the study of complex networks. • The shorter the rewiring period and the larger the rewiring proportion are, the better synchronized the network is. • Regardless of noise intensity and coupling strength, rewiring networks are always better synchronized than static networks. [ABSTRACT FROM AUTHOR]

To demonstrate and elucidate bursting patterns and their bifurcation mechanisms, a two-neuron Hopfield neural network is proposed in this paper. The proposed non-autonomous model has a time-varying equilibrium point whose stability undergoes continuous evolution in response to changes in stimulation, and exhibits chaotic dynamics, especially the quasi-periodic and periodic bursting patterns. Over a full bursting cycle, the stability evolution of the time-varying equilibrium point triggers Hopf bifurcation and fold bifurcation, leading to the emergence of quasi-periodic or periodic bursting. To elucidate the bifurcation mechanisms, the transitions between the spiking state and the resting state are demonstrated, thereby identifying the Hopf/Hopf quasi-periodic bursting and fold/fold/Hopf periodic bursting. In addition, a simple analog electronic circuit is designed for the physical implementation of the non-autonomous model, and a printed-circuit board based hardware circuit is made to test the experimental results to verify the numerical results. • Non-autonomous model of two-neuron Hopfield neural network considering stimulation is proposed. • Chaotic dynamics, quasi-periodic spiking/bursting patterns and periodic bursting patterns are exhibited. • Bifurcation mechanisms to quasi-periodic bursting and periodic bursting are elucidated theoretically. • Simple analog electronic circuit is designed and hardware circuit is made to test the experimental results. [ABSTRACT FROM AUTHOR]

Solving soliton equations on the time–space scale has always been a challenging issue. In this paper, we firstly generalize the Ablowitz–Kaup–Newel–Segur (AKNS) method to the time–space scale, concurrently obtain the nonlinear Schrödinger (NLS) equation on this scale, which unifies the continuous and the semi-discrete NLS equations. On this basis, the N -fold Darboux transformation is proposed for the NLS equation on a space scale. As applications, soliton, breather, and rogue wave solutions of NLS equation are derived from diverse seed solutions on a space scale. Specially, the rouge solution on a space scale is obtained for the first time. • The AKNS method is generalized to the time–space scale. • The NLS equation on a time–space scale is derived. • Continuous and the semi-discrete NLS equation are unified on a time–space scale. • Breather and rogue wave solutions of NLS equation are obtained on a space scale. [ABSTRACT FROM AUTHOR]

Self-sustained chaotic system based on active materials, where energy is absorbed directly from the environment to maintain one's own motion, furnishes an extensive scope of applications in energy harvesters, encrypted communication, bionic heart devices and other fields. This paper seeks to put forward a self-sustained chaotic pendulum system consisting of a liquid crystal elastomer fiber and a mass sphere under steady illumination. To investigate the self-sustained chaotic behavior of the pendulum system, we combine the dynamic liquid crystal elastomer model with principles of dynamics to establish the corresponding theoretical model of the system. Numerical results suggest that three typical motion modes, namely, static mode, self-sustained oscillation mode and self-sustained chaotic motion mode, are involved in the liquid crystal elastomer pendulum. The self-sustained motion is maintained by the work done by the contraction of the liquid crystal elastomer fiber with a light-blocking coating, which compensates for the energy dissipated by the damping. Furthermore, this study also explores the influences of five system parameters on the motion behavior of the LCE pendulum, and determines the key parameter values for the three distinct motion modes through detailed calculations and bifurcation diagrams. The present research findings demonstrate that introducing a new degree of freedom into the self-sustained periodic vibration system, it is possible to achieve self-sustained chaotic motion, providing significant insights into the development of self-sustained chaotic systems derived from active materials. [ABSTRACT FROM AUTHOR]

This paper focus on the effects of a codimension-2 non-smooth bifurcation on bursting behaviors in piecewise-smooth systems. A passive circuit with a switched power source is slightly modified by introducing a periodic exciting voltage to establish an example system of Filippov-type. By using Filippov's convex method, the sliding vector field is obtained, and the analytical solution of the sliding motion equation is derived. A codimension-2 non-smooth bifurcation, called "catastrophic boundary focus and catastrophic crossing-sliding bifurcation", is observed, and the unfolding of the bifurcation is discussed. Based on the bifurcation analysis, five bursting oscillations associated with the codimension-2 bifurcation are observed, and the dynamical mechanism is revealed. The study suggests that the bifurcation of boundary equilibrium can be neither a non-smooth fold one nor a persistence one if the sliding vector field is degenerate, and this bifurcation may also lead to jumping behaviors in a bursting. A non-smooth limit cycle may cross the switching manifold transversely, precisely at the boundary of the escaping subregion, causing the limit cycle to disappear catastrophically. This bifurcation of non-smooth limit cycle controls the transition between a quiescent state and a spiking state in a bursting. A grazing-sliding bifurcation in a slow–fast system can form "reentry sliding structures" in a bursting. [ABSTRACT FROM AUTHOR]

The asymmetric behavior of individuals plays a necessary role in the rapid development of human society. Typically, behaviors and acceptability of influential individuals exert influence on the strategy choices of others, but the influence flows mainly in one direction, which shows asymmetric emotions in the cooperative process. Based on this fact, this paper proposes a new prisoner's dilemma game model involving unidirectional acceptability on interdependent networks. Individuals with higher social influence are segregated spatially in upper network layers, while others with lower influence are located in lower network layers. And two parameters are introduced to the calculation of an individual's fitness in the model. Simulation results show that individuals who pay more attention to the average acceptability of individuals in the upper network layer promote cooperative behavior in the upper network layer in case of high temptation under unidirectional acceptability mechanisms. Moreover, the high coupling strength between interdependent networks promotes cooperative behavior in the system. In summary, these results may offer insights to underscore the pivotal role played by asymmetric emotion in promoting cooperation. • A new prisoner's dilemma game involving unidirectional acceptability on interdependent networks is proposed. • A distribution of location for individuals is related to social influence of individuals. • A sensitivity related to the network coupling strength can promote cooperation. [ABSTRACT FROM AUTHOR]

The Kirchhoff index is a novel distance-based topological index corresponding to networks, which is the sum of resistance distances between all pairs of nodes. It assumes a significant role in describing the flow of a network and can also characterize the stability of the network. The computation of the Kirchhoff index of a network is frequently performed through spectral analysis methods. However, for networks with irregular structures, this method may not be applicable. In this paper, we propose a polygon network model and calculate its Kirchhoff index by reconstructing the network construction process. Furthermore, by establishing the relationship between the known Kirchhoff index and the Laplacian spectrum of the network, we derive the Kirchhoff index of the network and its relationship with other network indices, such as the Global mean-first passage time and the average path length. We then perform calculations on these related indices to gain a more comprehensive understanding of the network. • The precise formula for the Kirchhoff index of Vicsek polygon networks is derived. • The relation between the Kirchhoff index and the first passage problem is established. • The ratio of resistance distance to distance is 2/3 for Vicsek 3-polygon. [ABSTRACT FROM AUTHOR]