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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]

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

• We consider both proportional delay and distributed delay, which are more difficult and need more challenging to calculation than the recent works. • Through designing impulsive controller, several novel sufficient conditions are given and rigorously proved to ensure that the heterogeneous dynamic NNs and the desired trajectory achieve quasi-synchronization. • Using the generalized formula for the variation of proportional delay and distributed delay parameters, the theoretical error bounded of quasi-synchronization is estimated. In this paper, we discuss the quasi-synchronization of delayed heterogeneous dynamic neural networks based on impulsive control. The main difference of this paper with previous works on quasi-synchronization is that both proportional delay and distributed delay are considered. By establishing a novel impulsive delay inequality, combining Lyapunov theory and the concept of average impulsive interval, some necessary items for quasi-synchronization of delayed heterogeneous dynamic neural networks are obtained. Moreover, through using the generalized formulae for the variation of proportional and distributed delay parameters, the theoretical error bounded of quasi-synchronization is estimated. Finally, numerical examples are listed to explain the validity of our results. [ABSTRACT FROM AUTHOR]

Cyclic dominance is observed in predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations and many other natural systems. Rock-Paper-Scissor(RPS) is a popular game which demonstrates cyclic dominance. In this paper, we investigate replicator dynamics of RPS-game under logistic growth functions with Allee effect. The results obtained are compared with the case of no Allee effect. Due to Allee effect the number of stable attractors increases in a certain parameter region. The obtained result can be interpreted biologically that diversity of an ecological system increases due to Allee effect. [ABSTRACT FROM AUTHOR]

• Being the first extensive numerical study of the dynamics of rock-paper-scissors type models with a total number of species (NS) between 3 and 12 having one or more (weak) species characterised by a reduced predation probability. • The demonstration, using lattice based spatial stochastic simulations with random initial conditions large enough for coexistence to prevail, that parity effects are significant in rock-paper-scissors models, specially if the number of species is smaller or equal to 8. • The verification that, despite the significant dispersion observed among individual models, weak species have on average higher abundances strong ones if the reduced predation probability is sufficiently smaller than unity, with the exception being of the four species case. We investigate the impact of parity on the abundance of weak species in the context of the simplest generalization of the rock-paper-scissors model to an arbitrary number of species — we consider models with a total number of species (N S) between 3 and 12, having one or more (weak) species characterized by a reduced predation probability (by a factor of P w with respect to the other species). We show, using lattice based spatial stochastic simulations with random initial conditions, large enough for coexistence to prevail, that parity effects are significant. We find that the performance of weak species is dependent on whether the total number of species is even or odd, especially for N S ≤ 8 , with odd numbers of species being on average more favourable to weak species than even ones. We further show that, despite the significant dispersion observed among individual models, a weak species has on average a higher abundance than a strong one if P w is sufficiently smaller than unity — the notable exception being the four species case. [ABSTRACT FROM AUTHOR]

In ecosystems, cooperative behavior is universal and can dramatically improve a species' chances of survival. Nevertheless, the situations that can occur when different species with cooperative tendencies interact are veiled. To explore such a situation, in this paper, we investigate how cooperative behavior can affect biodiversity in the population system. Based on the spatial rock–paper–scissors (RPS) game, which incorporates the relative power between predator and prey species, we redefine the competition rate to facilitate cooperative behavior. Competition rates are modulated by the sensitivity parameter, which regulates alterations in competition rates stemming from variations in predator–prey population disparities. Through comprehensive numerical analysis, we have demonstrated compelling evidence confirming the nature of cooperative behavior in maintaining biodiversity. The sensitivity parameter acts as a double-edged sword; it hampers biodiversity when it falls below a certain level. Conversely, when it exceeds the threshold, it supports the maintenance of biodiversity. From snapshots and the coefficient analysis based on spatial autocorrelation, we found that empty sites are essential to promote coexistence as resource nodes. Compared with previous studies in spatial RPS games, our findings suggest that simple modification of a competition rate rather than exploiting cooperative games can realize the cooperative behavior of cyclically competing populations, and biodiversity is sensitively affected by cooperation. • We define cooperative behavior between species by redefining competition rates. • Cooperation affects competition and exchange sensitively, affecting biodiversity. • Empty spaces play an important role and are crucial in promoting coexistence. [ABSTRACT FROM AUTHOR]

Complex systems in ecological science can be generally defined by either the number of different species or the structure among species having many relations, and understanding the given interaction structure is essential to predict the evolution of ecosystems. In this paper, we propose a multi-species system whose competition can occur cyclically. By exploiting the generalized system of cyclic competition among seven species, we explore how species biodiversity can appear when the generalized system is established by possessing the underlying mechanism of rock–paper–scissors (RPS) and rock–paper–scissors–lizard–spock (RPSLS) games. Through Monte-Carlo simulations, similar to the RPSLS system having the phase transition in biodiversity from five to one containing the three species survival in the middle, the model for seven species also exhibits similar cascading features in the biodiversity as mobility increases, validated by measuring the survival probability. We also found that not every cyclic structured system among seven species exhibits a common cascading feature in the transition in biodiversity. It is revealed that such a characteristic may require sufficient structures of RPS-like subgroups. Our findings may provide insights into the biodiversity of cyclically competing species and the link to predict biodiversity associated with the interaction structure in the microscopic framework. • Spatiotemporal evolution of cyclically competing seven species is investigated. • Species biodiversity depending on mobility exhibits the similar pattern of cascading dynamics. • Different pathways of cyclic competition among seven species can present different biodiversity. • Predicting biodiversity can be possible based on the competition structure among species. [ABSTRACT FROM AUTHOR]

• We derive a finite population spatial replicator dynamic for arbitrary games. • We analyze the effects of nite populations on generalized rock-paper- scissors. • We show the finite population spatial replicator dynamic destroys a trav- eling wave. We derive both the finite and infinite population spatial replicator dynamics as the fluid limit of a stochastic cellular automaton. The infinite population spatial replicator is identical to the model used by Vickers and our derivation justifies the addition of a diffusion to the replicator. The finite population form generalizes the results by Durett and Levin on finite spatial replicator games. We study the differences in the two equations as they pertain to a one-dimensional rock-paper-scissors game. [ABSTRACT FROM AUTHOR]

In previous works (Inaba and Kousaka, 2020; Inaba and Tsubone, 2020; Kato et al. 2022; Inaba et al., 2023), significant bifurcation structures referred to as nested mixed-mode oscillations (MMOs) were discovered in the forced Bonhoeffer-van der Pol (BVP) oscillator. Since the experimental discovery of MMOs, unnested MMO-incrementing bifurcations (MMOIBs) have been observed in numerous systems, including the Belousov–Zhabotinsky reaction, chlorite–thiosulfate reaction, and hydrodynamic and electrochemical systems; in such systems, daughter oscillations [ L 1 s 1 , L 2 s 2 × m ] can be observed for successive values of m. In this paper, we investigate high-order singly nested MMOs of the form [ C 0 , m , D 0 , m × p ] for increasing values of m , i.e., C 0 , m is followed by D 0 , m repeated p times, where C 0 , m ≡ [ C 0 , D 0 × m ] , D 0 , m ≡ [ C 0 , D 0 × (m + 1) ] , and C 0 and D 0 are adjacent fundamental MMOs, e.g., C 0 = 1 s and D 0 = 1 s + 1 . This work extends our previous analysis that was conducted on the lowest-order case (m = 1), and we demonstrate that the high-order (m ≥ 2) singly nested MMOs can indeed occur. We investigate the cases of m = 2 , 3 , 4 , and 10, although we note that the regions in which nested MMOs can be observed become increasingly narrow for larger values of m. These bifurcations are confirmed via one-parameter bifurcation diagrams, time-series waveforms, and first return plots. Furthermore, we present notable similarities between the Nagumo–Sato piecewise-linear discontinuous one-dimensional map and the forced BVP oscillator. • Nested mixed-mode oscillations (NMMOs) represent a significant bifurcation phenomenon. • It is known that parent–daughter processes generate [ C 0 , D 0 × m ] for successive m. • NMMOs generate [ C 0 , m , D 0 , m × p ] for successive p. • In the above notation, C 0 , m = [ C 0 , D 0 × m ] and D 0 , m = [ C 0 , D 0 × (m + 1) ]. • This paper shows that NMMOs occur for successive p and increasing values of m. [ABSTRACT FROM AUTHOR]

The existence, uniqueness, exponential stability with the trajectory (T-)controllability and optimal control results for mild solutions to the fractional neutral stochastic differential system (FNSDSs) are presented in this article. To demonstrate the results, the concept of bounded integral contractors combined with the regularity, a weaker notion of Lipschitz continuity, with stochastic approach and sequencing techniques are used. In contrast to previous publications, we do not need to specify the induced inverse of the controllability operator to prove the stability results, and the relevant nonlinear function does not have to meet the Lipschitz condition. Furthermore, exponential stability result for FNSDSs with Poisson jump via impulsive integral inequality is established following the trajectory (T-) controllability for higher-order FNSDSs via integral contractors with the help of Gronwall's inequality and the optimal control problem for higher-order FNSDSs via Balder's theorem. A numerical example is discussed to justify the theory. Finally, a filtration model and the real life stochastic Kelvin–Voigt and Maxwell models with the numerical simulation are demonstrated to satisfy the acquired results. This paper extends all previous works having the nonlinear Lipschitz continuous operators. • The wellposedness for the fractional neutral stochastic differential system are presented. • The concept of bounded integral contractors and sequencing technique are used. • Based on the editor request we study a new article called Trajectory (T-) Controllability of the proposed system. • T-controllability via Integral contractor is not available in the literature for the stochastic fractional system. • Then we study the optimal controllability. This paper is the unique combinations of all three concepts. • We do not need to match with the induced inverse of the controllability operator to prove the stability results. • The relevant nonlinear function does not have to meet the Lipschitz condition. • Integral contractor is a weaker notion of the Lipschitz continuity. • A real-life stochastic Kelvin–Voigt and Mexwell applications are demonstrated to satisfy the acquired results. • This paper extends all previous works in this direction. [ABSTRACT FROM AUTHOR]

In the last decade, hundreds of papers have been published on fractional modeling. The approach is often similar, with the motivation of incorporating a "memory effect": take the integer-order differential-equation model, and replace the ordinary derivative to the left-hand side by a fractional operator/derivative. Does this make sense? Which is the memory there? What is the physical and biological interpretation of fractional models? This paper aims at investigating these important issues. With fluxes, transitions, and concepts from survival analysis (hazard function), we give a meaning for Caputo compartmental models and their non-Markovian property. Essentially, a fractional index is connected with the instantaneous risk of leaving a compartment, conditioned on the past stay in there. We distinguish between Caputo models that are purely fractional (i.e., the usual ones) and partially fractional (i.e., a mix of ordinary and Riemann–Liouville components), and we explore initialization as well. We build new Euler-type numerical schemes, rooted in probability, and assess them for different models: a simple death process, logistic growth, SIR equations, the dynamics of an HIV infection, and the evolution of the smoking habit. A detailed discussion on the pros and cons of the fractional methodology is made along the article. • Which is the role of a fractional operator in an equation? What is memory? • The paper investigates these issues, for Caputo fractional compartmental models. • We analyze the hazard function (risk of transition), initialization, non-Markovianity. • Some Caputo models in the literature are unphysical. Critical evaluation is included. • Numerical experiments are conducted with probabilistic Euler-type discrete schemes. [ABSTRACT FROM AUTHOR]

The tracking problem of Julia sets of the SIS (Susceptible–Infectious–Susceptible) model with saturated healing function under noise perturbation is investigated. Firstly, a discrete version of the SIS model with saturated healing function and its Julia set are introduced. Secondly, the structure of the Julia set are discussed, and the result shows that the filled-in Julia set of this model can be presented as a bounded set with positive measure and an unbounded set. The numerical result shows that the measure of the latter is almost zero. Then, the tracking problem of the Julia sets for the SIS model with saturated healing function is proposed. To address this problem, differential dynamic programming (DDP) and model predictive control (MPC) are used to design controllers. Controllers with different objective functions are compared across their performance. At last, a metric for evaluating the tracking performance is suggested, and a more effective objective function is proposed based on this metric. • The structure of the Julia set is given. Many papers only discuss the shape of the Julia set by showing the figure of the Julia set. Few of them give a certain expression of the Julia set. However, in this paper, the structure of the Julia set is provided. • The tracking problem of the Julia set under noisy disturbance is proposed. The Julia set is important in distinguishing whether the value makes the system keep bounded. However, a small disturbance may cause the value in the filled-in Julia set to go out of the Julia set and finally tend to be infinite. The tracking problem of the Julia sets under noisy disturbance is introduced to keep the value in the filled-in Julia set. • The metric for tracking performance is proposed. To evaluate the tracking effect, the average tracking rate for single point and filled-in Julia set is proposed. It can numerically represent the difference between the Julia set under noisy disturbance and the Julia set without noisy disturbance. In addition, It can measure the difference between the value of iteration under noise disturbance and the value of iteration without noise disturbance. [ABSTRACT FROM AUTHOR]

The exponential stabilization of stochastic quantum systems (SQS) under time-delay noise-assisted feedback is addressed based on the exponential stability of the stochastic differential delay equation (SDDE) in this paper. We show that if the stochastic differential equation (SDE), which covers the dynamical models of SQS under noise-assisted feedback, is exponentially stable, then the corresponding SDDE is also exponentially stable when the time-varying delay is bounded by a positive number, which is given in an implicit expression and can be computed numerically. On this basis, the results for the general SDDE are applied to the SQS under time-delay noise-assisted feedback, and the corresponding time-delay boundary is obtained. Furthermore, we show the time-delay boundary in numerical simulations. • A upper bound on delay time that ensures exponential stabilization of SDDE is given. • The results from general SDE are applied to the stochastic quantum systems (SQS). • The results of this paper are suitable for a wide range of feedback strategies. • We present a way of studying exponential stabilization of SQS under delay feedback. [ABSTRACT FROM AUTHOR]

The slowly forced Duffing system has been found to exhibit unique fast–slow behaviors in descending frequency switching scheme, the typical of which is the sliding bursting, which is instructive for understanding the dynamics of ubiquitous frequency switching systems in scientific research and practical engineering. This paper is devoted to further refining the fast–slow dynamics of the slowly forced Duffing system with another commonly encountered frequency switching scheme, i.e., the ascending frequency switching, characterized by switching the frequency synchronously according to the increase or decrease of state variable values. Taking the forcing amplitude as an example, this paper provides a theoretical way to fully summarize the fast–slow behaviors in frequency switching systems with the variation of parameter values based on the proposed superposition analysis of one- and two-parameter bifurcations of subsystems. As a result, two typical bifurcation structures and eight threshold windows with distinct switching vector fields therein are identified, inducing up to ten different bursting patterns. Among them, several novel fast–slow dynamics, such as multiple jumps hysteresis loop formed by boundary equilibrium bifurcations and the switching failure phenomena, are presented and investigated. In particular, the underlying mechanism of threshold modulation, i.e., the evolution of unconventional bifurcations, is also found. These findings contribute to complementing and contrasting the existing studies on the fast–slow dynamics of frequency switching systems. • Theoretical way for identifying threshold windows under different parameter values. • Novel bursting patterns induced by several novel multi-jump hysteresis loops. • Underlying mechanisms of the threshold modulating the dynamical behaviors. • Effect of frequency switching scheme and system parameters on the fast–slow dynamics. [ABSTRACT FROM AUTHOR]

Hammerstein structure is commonly used for describing nonlinear dynamic characteristics, and its identification is a basic premise of nonlinear system analysis and control. This paper investigates online identification methods for a class of Hammerstein nonlinear systems, which consists of a nonlinear memoryless element followed by a linear output-error subsystem. The unmeasurable noise-free output of the linear subsystem makes the model parameters cannot be directly estimated by traditional identification methods. To address this difficulty, by using a series of weighted particles to adaptively approximate the posterior probability density function of the unmeasurable noise-free output, this paper proposes a particle filter-based stochastic gradient algorithm. Moreover, to enhance the data utilization and estimation accuracy, a particle filter-based multi-innovation stochastic gradient algorithm is developed through the innovation expansion technique. The simulation results demonstrate that compared with the existing benchmark algorithms, the proposed algorithms need a little more computational time due to the introduction of the adaptive particle filter, but they have the improved identification accuracies. [ABSTRACT FROM AUTHOR]

Noise, as a form of destructive signal interference, brings challenges of varying degrees in the field of wireless communications. In order to reduce the impact of noise on the communication system, this paper combines four kinds of noise reduction schemes to compare and analyze the anti-noise performance in the communication system. In this paper, a chaotic keying system based on carrier modulation is firstly proposed as the basis, which can implicitly propagate an extra part of bits to improve the transmission rate. The system is compared with other systems through formula derivation and simulation analysis to analyze the advantages brought by carrier modulation. Next, four noise reduction schemes, namely, moving average (MA) noise reduction, autocorrelation (AC) noise reduction, variational modal decomposition (VMD) and wavelet packet decomposition (WPD), are combined to compare and analyze the performance of each scheme. By improving or balancing the advantages of some of the schemes, the overall performance is more obviously improved. Finally, LDPC channel coding is introduced, and the anti-noise performance of the communication system after the introduction of LDPC coding is analyzed through Monte Carlo simulation. After all the above simulations, the carrier modulation can efficiently improve the system transmission rate, which is the best choice for today's high-speed communication. The four noise reduction schemes can effectively improve the anti-noise performance of the system, each has its own advantages and disadvantages, and the performance is better after improvement and balancing. After the introduction of the LDPC coding, the performance of the system has a qualitative leap, which provides a reference for the future research. All the above schemes have good theoretical value and can provide good reference for practical engineering applications. • A superior chaotic system is proposed to be used as a test system for detecting the effects of signal processing schemes. • The noise reduction effects of the four schemes when applied to chaotic system are proposed and comparatively analyzed. • The paper introduces LDPC code and explores its combination with the chaotic system. [ABSTRACT FROM AUTHOR]

In recent years, the connection between emotions and cooperative behavior has received widespread attention. Aiming at the limitations of the emotional state hypothesis in the traditional spatial evolutionary game model, this study introduces a novel memory-based emotion mechanism. By treating emotion as a variable that can be measured and accumulated, and incorporating it into a network reciprocity model, this paper explores how emotion affects cooperative behavior in social dilemmas with different dilemma strengths. It is worth noting that the accumulated length of memory for emotions is variable. Using Monte Carlo simulation, the study analyzed the roles of positive and negative emotions in three social dilemmas and their specific effects on cooperative tendencies. The findings of this paper emphasize the importance of emotional dynamics and suggest that emotions can address some difficult problems. We propose potential applications of this mechanism in social governance and policymaking. • Introduce a memory-based emotion mechanism into network reciprocity, which quantifies and accumulates emotions as factors influencing cooperative behavior. • Emotions emerge along with the process of comparison with local neighbors, with the length of memory being variable. • Emotions are categorized as positive and negative. Positive emotion can facilitate emergence of cooperative behavior, while negative emotion makes the evolution of cooperation more difficult. • From the analysis of dilemma strength across various models, it is evident that integrating emotion into evolutionary games can solve the dilemma problem. [ABSTRACT FROM AUTHOR]

Manakov and Santini had studied the formal solutions and utilized the Riemann–Hilbert (RH) dressing method to investigate longtime behavior of the solutions and asymptotical implicit solutions of Pavlov equation (Manakov and Santini, 2007) and heavenly equation (Manakov and Santini, 2006). In the paper, we introduce a new Lax pair to construct an integrable system, which can be reduced to the standard Pavlov equation. Therefore, we refer to it as a generalized Pavlov equation. By utilizing the inverse scattering transform (IST) technique, we successfully derive the general formal solutions for the general Pavlov equation. Additionally, through the construction of a new RH problem, we investigate the longtime behavior of the solutions to the general Pavlov equation. The results presented in this paper expand upon the results previously presented by Manakov and Santini in their work (Manakov and Santini, 2007). [ABSTRACT FROM AUTHOR]

In this paper, we create the rumor propagation model with diffusion behavior by considering the state of the rumor in both the time dimension and the space dimension comprehensively. Meanwhile, we demonstrate the reaction–diffusion model using Turing patterns after determining the prerequisites for their occurrence. In order to achieve the purpose of predicting and controlling rumors in time, we choose to utilize the parameter identification technique based on the Barzilai–Borwein (BB) algorithm and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. In the numerical simulation section, we first investigate how the rumor avoidance rate and cross-diffusion coefficients affect the propagation of rumors. Then, based on a continuous spatio-temporal system and complex network system, respectively, we perform parameter identification for the propagation model. We thoroughly examine how the type of algorithm, the quantity of unknown parameters, and the network structure affect the identification outcomes in terms of the cost function, error curve, and program function time. When the model constructed in this paper is used for parameter identification on different network structures, the error gap between the final value and the target value is not significant. However, the cost function and time consumption for parameter identification on complex networks are much smaller than on the continuous medium. • This paper is based on a rumor propagation system with diffusion behavior. • We further analyze the parameter identification based on the optimal control theory. • We explore the different factors that influence the results of parameter identification. [ABSTRACT FROM AUTHOR]

Modern power grids, functioning as a cyber-physical system (CPS), accommodate high penetration level of distributed generations (DGs) to ensure sustainability. Achieving sustainability through grid-scale DGs, however, increases the likelihood of islanding occurrences, which jeopardizes a major parameter of CPS implementation: security. This paper proposes an artificial intelligence-based approach for detecting islanding in modern power grids. The method utilizes measured voltage and frequency to develop a fuzzy center of gravity (COG)-based equivalent model of the system. The model is derived by combining data collected from phasor measurement units (PMUs) with fundamental dynamical equations that govern power system dynamics. In this model, the system is represented using a set of fictitious reactances calculated using goal programming, which are then utilized to connect the COG to the local centers of inertia (COIs). By having a set of fictitious reactances for various operating points fed into a fuzzy model, one could develop an online model to calculate the fictitious reactances with high accuracy and speed at specific snapshots. By incorporating the maximum allowable phase differences between areas into the COG model to ensure transient stability, one could enhance the developed model to be robust against cyber-physical contingencies and cyber-attacks, albeit at the expense of a slight reduction in accuracy. The calculated fictitious reactances, represented in terms of local frequencies throughout the system, serve as valuable indicators for detecting islanding. By classifying the calculated fictitious reactances using support vector clustering over a period of time, islanding could be detected with high accuracy. Furthermore, incorporating the COG concept with the clustering based on fictitious reactances makes it possible to detect false data injection in an area of the system. The efficacy of the proposed method is assessed using simulated data from the renewable integrated 73-bus IEEE test system. • This paper deals with the application of computational intelligence for stability assessment of large-scale power systems. • Data-driven based approach is proposed to detect islanding occurrence. • A combination of Fuzzy-modeling and support vector clustering is used to propose a fast and accurate farmwork. • The highly non-linear model of power system is represented using a combination of COIs and center of gravity. [ABSTRACT FROM AUTHOR]

Uncertain differential equation is a type of differential equation involving uncertain processes. This paper analyzes a simple pendulum system with a varying drag coefficient by the tool of uncertain differential equation, and derives the uncertain simple pendulum equation. Afterwards, the numerical method of solving the uncertain simple pendulum equation and its parameter estimation method are given in this paper. Finally, a real-world example is provided to illustrate the uncertain simple pendulum equation. [ABSTRACT FROM AUTHOR]

Nonlinear dynamical systems excited by combined Gaussian and Poisson white noises are widely found in the scientific field. However, the introduction of Poisson white noise results in the associated forward Kolmogorov equation becoming an integro-differential equation (IDE), which makes it difficult to solve the response of these dynamical systems. At present, traditional numerical IDE solvers are limited due to both the mesh generation and high computational costs. In this context, this paper integrates the multi-element Gauss–Legendre (GL) quadrature into the physics-informed neural networks (PINNs) algorithm to predict the response of systems excited by combined Gaussian and Poisson white noises. A residual-based adaptive distribution (RAD) sampling method, which replaces Latin hypercube sampling (LHS) method, is implemented to adjust the residual points to improve the accuracy and training efficiency of the proposed algorithm. The results demonstrate that the integration of the PINNs algorithm with RAD sampling method dramatically enhances the tolerance of noisy data and expedites the convergence of the PINNs algorithm compared with the LHS sampling method. It has the ability to achieve better performance in a shorter training time and reduces the demand for data during the training process. Additionally, the Monte Carlo (MC) simulation is carried out to demonstrate the effectiveness of the numerical results in this paper. • A deep neural network algorithm is proposed to predict the response of the system. • The Gauss–Legendre quadrature is integrated to solve the forward Kolmogorov equation. • A residual-based sampling approach enhances the convergence of our algorithm. • Two examples are worked out to illustrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

The multi-layer perceptron architecture in PINNs model severely limits the model's ability to learn the temporal evolution of equation features. Instead, the GRU network is capable of capturing these complex temporal correlation features. This paper replaces the multi-layer perceptron structure of the PINNs model with the GRU network and called the modified model as physics-informed gated recurrent units network method (PGNM model). The PGNM model exhibits enhanced performance in assimilating insights from historical data and providing accurate predictions for future data. This paper compares the predictive performance of the proposed PGNM model and the classical PINNs model using L2 error and mean squared error (MSE) as metrics. Additionally, it evaluates how altering various parameter settings, such as the number of neurons, hidden layers and iterations, affects the predictive capabilities of both models. In conclusion, PGNM model shows significant improvement in prediction accuracy compared to PINNs model. Furthermore, PGNM model achieves better long-range prediction results than PINNs model when the training data does not include samples from the time period to be predicted. [ABSTRACT FROM AUTHOR]

This paper investigates the Sundaresan technique for modeling fractional order systems. Sundaresan, Prasad, and Krishnaswamy published this method in 1978 for modeling oscillatory and non-oscillatory systems based on the second-order integer transfer function. This technique is based on the transient response parameters. A problem of convergence of the derivative of the response in the frequency domain makes it impossible to follow Sundaresan's solution in his original paper with integer order when it is a fractional order case. The paper proposes an equation that outlines this problem. Due to the limited knowledge of the inverse Mittag-Leffler function, a reduced form of this equation is explicit to avoid the inverse problem. Results with simulated and real curve shapes show that the method works well, with a good approximation to the curve, both with simulation and real system curves. • Develop an equation for fine-tuning the parameters of the pseudo-second-order system. • Novel fractional-order identification based on Sundaresan technique. • The method proposed is a generalized method of the classic Sundaresan technique. [ABSTRACT FROM AUTHOR]

The object of this study is to define existence, controllability and exponential stability results within a Sobolev-type fractional stochastic neutral equations of order 1 < ω < 2 with sectorial operator and optimal control. To do this, first, this study relies on the confluence of stochastic analysis, fractional calculus, sectorial operator, and the applicability of Sadovskii's fixed point method. First, we highlight the existence of mild solutions to the fractional stochastic control equation and then introduce the concept of approximate controllability. Next, employing an impulsive Poisson system yields sufficient conditions for guaranteeing the exponential stability of the mild solution in the mean square moment. Further, our inquiry expands into the existence of optimal control. Finally, an example is provided to illustrate the obtained theory. • This paper explores the stability of the fractional delay system of order ω ∈ (1 , 2). • This paper is the first study of a fractional jumps system with sectorial operators. • We establish conditions for the fractional system and extend to the controllability. • We determine mean square stability of fractional system ω ∈ (1 , 2) with Poisson jumps. • Finally, an optimal control pair is provided to show the solvability of the problem. [ABSTRACT FROM AUTHOR]

This paper creatively proposes a type of cubic fractal matrix and a new spatiotemporal chaotic system named logistic-logistic cascade coupled map lattice (L-LCCML). Furthermore, based on cubic fractal matrix and L-LCCML, this paper proposes a novel image encryption algorithm. The proposed cubic fractal matrix is three-dimensional, irregular, and self-similar. In particular, the proposed L-LCCML system adopts cascade coupling parameter to ensure the dynamic effect of coupling. Therefore, L-LCCML has excellent chaos and is suitable for information encryption. To provide a more secure approach, the proposed algorithm contains two diffusion operations, one permutation operation, and does not require multiple rounds of encryption. The diffusion operation is based on the cubic fractal matrix, which has good security and high encryption efficiency. In addition, the algorithm adopts sorting permutation based on L-LCCML, which provides good randomness for encryption. Experimental results show that the proposed algorithm has the characteristics of large key space, high sensitivity, fast encryption speed, good statistical properties of cipherd images, and etc. Therefore, the proposed algorithm is a usable alternative for practical secure communication. [ABSTRACT FROM AUTHOR]

This paper focuses on solving a stochastic saddle point problem (SPP) under an overparameterized regime for the case, when the gradient computation is impractical. As an intermediate step, we generalize Same-sample Stochastic Extra-gradient algorithm (Gorbunov et al., 2022) to a biased oracle and estimate novel convergence rates. As the result of the paper we introduce an algorithm, which uses gradient approximation instead of a gradient oracle. We also conduct an analysis to find the maximum admissible level of adversarial noise and the optimal number of iterations at which our algorithm can guarantee achieving the desired accuracy. • Generalized the S-SEG algorithm to a biased oracle. • Specified the result with Uniform Sampling and Importance Sampling based algorithm. • Proposed Zero-Order Same-sample Stochastic Extragradient algorithm for SPP. • Corroborated our theoretical results with experimental testing. • Compared our algorithm with several other algorithms, used for the solution of SPP [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]