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Currently, many existing image encryption algorithms have encountered challenges in achieving robustness and efficiency, mainly due to insufficient scrambling or inadequate diffusion mechanisms. These limitations can lead to vulnerabilities, making encrypted images more susceptible to attacks and reducing overall security. To address these issues, this paper proposes a new image encryption algorithm (MCLCM-IEA) based on a novel two-dimensional hyperchaotic map (2D-MCLCM). This algorithm integrates a difference algorithm during diffusion and a double-pointer algorithm during scrambling. Additionally, to enhance the security of cipher images, we introduce a plaintext-related weight matrix, which not only expands the key space of MCLCM-IEA but also strengthens its overall security. Benefiting from the superior chaotic properties exhibited by 2D-MCLCM, the strong diffusion efficiency got from the difference diffusion algorithm, and the effective scrambling provided by the double-pointer algorithm, MCLCM-IEA performs exceptionally well in simulation experiments. The results demonstrate that MCLCM-IEA can effectively resist various illegal attacks and showcase robust security and high efficiency. [ABSTRACT FROM AUTHOR]

The initial segmentation phase is crucial in image processing to simplify the image representation and extract some desired features. Different methods and techniques have been proposed for image multi-level thresholding, but they are still stuck in local optima and need improvement. Recently, a metaheuristic optimization algorithm called Golden Jackal Optimizer (GJO) has been proposed as an alternative solution. The GJO has been adopted as a good solution for many optimization problems. However, the GJO attempted to solve the convergence problem to a local minimum during execution, often leading to unsatisfactory results. Most variants of GJO are based on chaotic systems due to their easy implementation and remarkable capacity to avoid being trapped in local optima. This paper proposes a Polynomial Chebychev Symmetric Chaotic-based GJO (PCSCGJO) algorithm by combining a recently developed chaotic generating function to achieve better segmentation results. This variant improves the GJO by introducing the chaotic generating function of the Chebyshev polynomials as an update process while searching for the optimal solution. Simulation results prove the effectiveness of the PCSCGJO method and its ability to deal with different medical color images. The quality of the segmented images obtained by the proposed method was compared to well-known metaheuristic algorithms using performance metrics such as PSNR, SSIM, FSIM, and MSE. Consequently, the metrics values show that the suggested technique outperforms the other methods regarding quality and accuracy. [ABSTRACT FROM AUTHOR]

This paper provides an overview of the results obtained from the study of adaptive dynamical networks of Kuramoto oscillators with higher-order interactions. The main focus is on results in the field of synchronization and collective chaotic dynamics. Identifying the dynamical mechanisms underlying the synchronization of oscillator ensembles with higher-order interactions may contribute to further advances in understanding the work of some complex systems such as the neural networks of the brain. [ABSTRACT FROM AUTHOR]

Using chaos for communication can provide more robust channel security, covert transmission, and inherent support for spread-spectrum modulation. Although numerous studies have explored this technology, its practical deployment remains limited due to substantial hardware demands, complex signal processing, and a lack of efficient modulation methods for chaotic signals. In this study, a novel chaotic digital communication system is proposed and studied. A prototype of a frequency-modulated antipodal chaos shift keying (FM-ACSK) system is implemented on an Intel Cyclone V field-programmable gate array (FPGA) along with a complete mathematical model using Matlab R2022a Simulink software. Using FPGAs to implement chaotic oscillators avoids analog system problems such as component drift and high thermal instability while providing determined system parameters, rapid prototyping, and high throughput. The employment of FM over a chaotic modulation layer provides a passband operation (currently at an intermediate frequency of 10.7 MHz) while adding the benefits of carrier frequency offset robustness and constant signal envelope. Within this study, the robustness of FM-ACSK to white noise in the channel was evaluated using bit error rate, which was tested through hardware experiments and simulations. The results show the feasibility and potential performance limitations of this approach to chaotic communication system design. [ABSTRACT FROM AUTHOR]

Currently, despite advances in the analysis of dynamical systems, there are still doubts about the transition between both stable and chaotic behaviors. In this research, we will explain the transition of a system that develops between two dynamic systems that have already been studied: the classical logistic model and a new chaotic system. This research addresses the study of the transition of both the system and its behaviors using computational techniques, where cobweb diagrams, time series, bifurcation diagrams, and even a graphical visualization for the maximum Lyapunov exponent will be visualized. Using a graphical and numerical methodology, bifurcation points were identified that revealed the transition of behaviors at different points. This resulted in a deep understanding of the dynamics of the system, thus highlighting the importance of incorporating computational analysis in dynamic systems, which greatly contributes to the efficient modeling of natural phenomena. [ABSTRACT FROM AUTHOR]

We investigate the synchronization dynamics of two non-identical, mutually coupled Rulkov neurons, emphasizing the effects of coupling strength and parameter mismatch on the system's behavior. At low coupling strengths, the system exhibits multistability, characterized by the coexistence of three distinct 3-cycles. As the coupling strength is increased, the system becomes monostable with a single 3-cycle remaining as the sole attractor. A further increase in the coupling strength leads to chaos, which we identify as arising through a novel type of intermittency. This intermittency is characterized by alternating dynamics between two low-dimensional invariant subspaces: one corresponding to synchronization and the other to asynchronous behavior. We show that the system's phase-space trajectory spends variable durations near one subspace before being repelled into the other, revealing non-trivial statistical properties near the onset of intermittency. Specifically, we find two key power-law scalings: (i) the mean duration of the synchronization interval scales with the coupling parameter, exhibiting a critical exponent of − 0.5 near the onset of intermittency, and (ii) the probability distribution of synchronization interval durations follows a power law with an exponent of − 1.7 for short synchronization intervals. Intriguingly, for each fixed coupling strength and parameter mismatch, there exists a most probable super-long synchronization interval, which decreases as either parameter is increased. We term this phenomenon "dragon intermittency" due to the distinctive dragon-like shape of the probability distribution of synchronization interval durations. [ABSTRACT FROM AUTHOR]

Recently, memristive Hopfield neural networks (MHNNs) have received considerable attention in designing chaotic systems with complex dynamics because of their distinctive connectivity structures and memory properties. However, the literature rarely reports on the integration of discrete memristors with HNNs and the subsequent observation of their dynamical behavior. Based on the synaptic plasticity of memristors, this paper constructs a novel three-dimensional discrete memristive Hopfield neural network (3DDMHNN) model based on discrete memristor simulating self-synapse. Such a new neural network can exhibit chaotic attractors with different topological structures. Analysis reveals that the phase diagrams produced by the 3DDMHNN display several phenomena, including the formation of multi-ringlike volumes, attractor growth, hyperchaotic attractors, periodic offset behavior, and infinite coexistence of initial value offset behavior. To confirm the physical existence and feasibility of the 3DDMHNN, a simulation circuit incorporating a discrete sinusoidal memristor and the 3DDMHNN was designed. Meanwhile, the 3DDMHNN is realized based on a DSP hardware platform. With the pseudo-randomness of the 3DDMHNN confirmed by relevant tests, the potential directions for its future applications have been significantly broadened. [ABSTRACT FROM AUTHOR]

The studies on Nonlinear Phenomena have been carried out in buck converter controlled by three different types of modulation technique—Peak current, Peak V2 and Enhanced V2. These three modulation methods are rippled based control methods as inductor current ripple is used in Peak current modulation (PCM) method and output ripple voltage used in both Peak V2 and Enhanced V2 modulation methods and due to that all three modulation methods provide fast dynamic response. Here three modulation techniques have been explained in details and simulation results have been provided. For designing the modulators—we consider two loops i.e. inner loop or fast feedback path (FFBP) and outer loop or slow feedback path (SFBP). The outer loop of all these three modulation methods contains same information, the difference between reference voltage and output voltage. Mathematical model has been developed with the help of state space equation in continuous conduction mode (CCM). Bifurcation diagrams are obtained with load resistance, input voltage and reference voltage as bifurcation parameter. To validate the bifurcation pattern, time plot and phase plane trajectory at each transition have been shown for these three types of modulated system. A comparative study has been made. Experiments are conducted on an enhanced V2 modulated buck converter to validate the nature of the nonlinearities. To check the dependency of the system on ESR value, parameter space plots are developed and compared for all these three types of control technique. [ABSTRACT FROM AUTHOR]

Securing image transmissions has become critical as the demand for image sharing and storage grows. In some commercial uses, in order to achieve a balance between encryption security and efficiency, some researchers have tried to encrypt only the region of interest of the user in the image. In order to accurately encrypt region of interest images, this paper proposed a region of interest image encryption algorithm based on lifting scheme and object detection. The algorithm automatically identifies the region of interest in the image and encrypts it securely and effectively. Firstly, the region of interest in the image is detected using the object detection model, and the non-maximum suppression algorithm is modified to solve the problem that the detection box outputted by the object detection model does not completely contain the region of interest. Then the existing pixel extraction method for region of interest images is improved to extract the pixels from the region of interest images at a faster speed, which improves the overall efficiency of the algorithm. Finally, based on the thought of wavelet lifting transform, combined with chaotic system, a two-layer hybrid lifting scheme encryption algorithm is proposed to encrypt the extracted pixels. Experimental results and security analysis show that the algorithm proposed in this paper can effectively protect all objects at once with high security. [ABSTRACT FROM AUTHOR]

In this study, we explore the dynamics of a plankton–fish system in which external toxic substances have adverse impacts on the plankton populations as well as the fish communities. Fish population is assumed to grow in a logistic fashion due to food sources other than zooplankton, and is being harvested at a nonlinear rate. Mathematically, we analyze the system for the feasibility and stability of the ecologically meaningful equilibria. We also obtain criteria for the optimal harvesting policy of the fishery resources. We modify the considered model to encapsulate the effect of negative feedback time delay involved in the growth of the fish population. By considering this time delay as a bifurcation parameter, we derive conditions for the existence of Hopf bifurcation; direction and stability of the bifurcating periodic solutions are also discussed. Extensive numerical simulations are done for the systems with and without time delay. The environmental toxins are found to affect the equilibrium abundances of plankton and fish population in the aquatic system. In the absence of time delay, we observe that the growths in fish population due to uptake of zooplankton and other food sources have potential to suppress the chaotic disorder and bring forth stability in the ecosystem. On the other hand, the excessive growth of phytoplankton due to overloading of nutrients and the increasing carrying capacity of the ecosystem for the fish population are found to exhibit destabilizing roles on the system's dynamics. Finally, we observe that the larger magnitude of negative feedback time delay in the growth of fish population drives the system to a chaotic zone. [ABSTRACT FROM AUTHOR]

In this paper, a quad-trophic food chain model with Beddington–DeAngelis functional response is formulated by incorporating fear effect and prey refuge. Firstly, it is proved that the system is dissipative. Five types of equilibria are identified, and the criteria for local and global stabilities of the coexistence equilibrium are deduced by Routh–Hurwitz criteria and Li–Muldowney geometric approach. Secondly, multiple bifurcations are explored. It is shown that the system undergoes transcritical bifurcation and pitchfork bifurcation by the Sotomayor’s theorem, Hopf Bifurcation by normal form theory, heteroclinic bifurcation and homoclinic bifurcation by stability analysis of manifolds. Moreover, we present numerical experiments to verify the correctness of theoretical analysis. In particular, it is observed that the system undergoes period doubling and period halving cascades, cataclysm, and quasi periodic bifurcation (a torus), thereby entering or escaping chaotic state. It is also observed a saddle-focus homoclinic loop, a period two saddle-focus homoclinic loop, and a period three saddle-focus homoclinic loop for the system. Finally, it is found that fear effect and prey refuge can stabilize the system. [ABSTRACT FROM AUTHOR]

Introduction: The gear-bearing system plays a critical role in turbo-machinery. Nonlinear dynamics of the system, particularly the suspension effects, gear mesh forces, and temperature-dependent viscosity, significantly influence its performance. Understanding the system’s behavior, especially under varying rotational speeds and temperatures, is essential to avoid catastrophic failures. This study investigates the nonlinear dynamic behavior of a pinion/gear system under such conditions. Purpose: The purpose of this study is to systematically analyze the nonlinear dynamic behavior of a gear-bearing system, considering the effects of nonlinear suspension, nonlinear oil-film forces, nonlinear gear mesh forces, and temperature-dependent viscosity. The study aims to identify chaotic motions and other dynamic behaviors under various operational conditions. Methods: The nonlinear dynamic equations governing the system are solved using the fourth-order Runge–Kutta method, with a time step of π/300 and a convergence criterion of less than 0.0001. Several analytical tools, including bifurcation diagrams, dynamic trajectories, Poincaré maps, Lyapunov exponents, and fractal dimensions, are used to analyze the system’s behavior. The bifurcation control parameters include the dimensionless rotational speed ratio, unbalance parameter, and damping ratio, with a focus on different temperatures (T = 25 °C, 40 °C, 50 °C, and 80 °C). Results: The study finds a wide range of dynamic behaviors, including periodic, sub-harmonic, and chaotic motions. The bifurcation diagrams indicate transitions from irregular to regular motions at various rotational speeds, with non-periodic motions observed at higher speeds. The Poincaré maps and Lyapunov exponents confirm the onset of chaotic behavior, particularly at certain rotational speeds and temperatures. The dynamic responses of the gear and bearing geometric centers are often non-synchronous, with synchronization occurring at specific points. Temperature increases result in the degradation of lubrication and larger vibration amplitudes, especially at high speeds. Discussion: The findings highlight the importance of considering temperature-dependent viscosity in dynamic analyses. Neglecting temperature effects, particularly at low rotational speeds, can significantly underestimate the system’s dynamic behavior. The non-synchronous dynamic behavior of the bearing and gear centers under varying operational conditions emphasizes the need for careful selection of parameters such as damping ratio and unbalance to avoid chaotic motions. These results provide valuable insights into the design and optimization of gear-bearing systems, ensuring reliability and extending service life. [ABSTRACT FROM AUTHOR]

There is some debate as to whether intransitive or transitive competition dominates natural communities (Soliveres et al., 2015; Shipley and Keddy, 1994). Certainly, in relatively large communities, it would be unlikely that either form could be completely avoided, leading to the issue of communities containing both transitive and intransitive elements. Based on a study of ants in coffee agroecosystems (Vandermeer and Perfecto, 2023; 2024), it has been noted that a strong intransitive loop seems connected to several transitive elements, in a formulation wherein a transitive "tail" is "recoupled" to a basic intransitive loop. Elaborating some theoretical consequences of this qualitative structure, when species numbers are odd, either the ultimate or penultimate species goes extinct, leaving a community of an intransitive structure with a transitive tail, with no recoupling to the intransitive part. When species numbers are even, on the other hand, increased recoupling results in a Hopf bifurcation, then expanding limit cycles, then chaos, and finally a heteroclinic cycle. [ABSTRACT FROM AUTHOR]

Advertising and promotion strategies are crucial marketing tools for increasing sales. In this paper, we primarily investigate the mathematical mechanisms for increasing sales by inducing a single-parameter sales promotion strategy into a differential advertising model. Based on the continuous model, we derive the discrete governing system for sales. By leveraging the existence, stability, and bifurcation and chaotic behavior of fixed points of the discrete system, we have elucidated the dynamic behavior of sales in the continuous model. The specific parameter ranges for the existence of a T-period solution and its stability conditions are given. Furthermore, we perform a flip bifurcation analysis of the positive fixed point. This analysis helps us to obtain the existence and stability conditions for nT-period solutions. Interestingly, for the same model, when we take different parameter values, flip bifurcation and inverse flip bifurcation can coexist. The bifurcation provides a route to chaos. In the simulations, we find that in some situations, there exists a pathway for the system to enter into chaos from a stable state through flip bifurcation, and then enter into a stable state through inverse flip bifurcation, while in other situations, there exists no such pathway. We propose an effective control strategy that serves to suppress flip bifurcation and promote inverse flip bifurcation to eliminate chaos. These findings have significant theoretical implications and practical applications in relevant markets. [ABSTRACT FROM AUTHOR]

Gestation is a very significant phenomenon in predator-prey dynamics. It influences the future predation rates and the growth of species. Gestation is the period of development of an embryo or fetus in a female mammal, from conception to birth. It plays a critical role in population dynamics and reproductive strategies in ecological studies. This article presents a comparative study of eco-epidemic models with and without time delay terms. The model takes into account a prey-predator system, dividing the prey population into susceptible and infected compartments. This article incorporates a time delay into the predator growth term to represent gestation delay. This article investigates the impact of time delay as a gestation delay on the model's dynamics and compares the results with those of the non-delay model. Our analytical and numerical studies reveal that the time delay stabilizes the model, exhibits switching behaviour, and leads to chaotic behaviour through periodic doubling. Moreover, the gestation delay destabilizes the model by causing Hopf bifurcations to emerge at multiple points. Our findings indicate that the delay model has richer dynamics than the non-delay model. The numerical simulations using MATLAB, along with the DDE-biftool and Matcont packages, illustrate the bifurcation analysis, phase portraits, and time series plots for both models. Our findings highlight the significant effects of gestation delay on the dynamics of eco-epidemic models. [ABSTRACT FROM AUTHOR]

Hamiltonian maps are considered a class of dynamical systems that hold meticulous properties used to model a large number of complex dynamical systems. When time flows in dynamical systems with two-dimensional degrees of freedom, the trajectories in phase space can be analyzed within bidimensional surfaces known as Poincaré sections. The Chirikov–Taylor standard map for two canonical dynamical variables (momentum and coordinate) is the most renewed map characterized by a family of area-preserving maps with a single parameter that controls the degree of chaos. In this study, a generalization of the standard map for two different problems is presented and discussed. The first problem deals with the higher-order derivative Hamiltonian system (up to the fourth order) since the fourth-order characteristic provides the possibility of chaotic behavior at all scales including nanoscales where high-order derivatives take place in nanosystems. The second problem concerns the time-dependent δ -kicked rotor in fractal dimensions characterized by a time-dependent potential due to its important implications in quantum chaos. This study shows that higher-order derivative maps and fractal dimensional δ -kicked rotor maps apparently exhibit a large number of chaotic orbits and fractal patterns, including the spiral fractal patterns comparable to the Julia set. Moreover, these problems are characterized by additional parameters which can be used to control chaos. Some of these parameters lead to chaos, and others lead to fractal patterns. [ABSTRACT FROM AUTHOR]

Given the large volumes of sensitive information transmitted over the Internet, digital signatures are essential for verifying message authenticity and integrity. A key challenge is minimizing computationally intensive operations, such as modular inverses, without compromising security. In this research, we propose the DSADH algorithm, which introduces a confusion step directly into the signature itself, rather than only applying it to the message, using a dynamic substitution box. It is generated with the number pi and changes with each signing. In addition, to enhance security, this work uses a 2048-bit prime, double the length frequently used. This proposal induces chaotic behavior in the signature, making it highly sensitive to any changes in the signer's private key or message content, thereby enhancing authentication and integrity verification. Moreover, the proposed algorithm computes a single multiplicative modular inverse during verification and none during signing, unlike other approaches that require inverse computation in both stages. Since the required inverse is for the Diffie-Hellman session key, it always exists and can be precomputed per communication rather than per message. Consequently, DSADH is on average 45 times faster than DSA. Additionally, we introduce a method to assess signature security by constructing images from signature bytes generated by slight changes to the signer's private key and message. Then, their chaotic behavior is evaluated with cryptographic metrics. [ABSTRACT FROM AUTHOR]

This study presents a novel approach by implementing an active memristor in a hyperchaotic discrete system, based on a cubic map, which is implemented by using two different microcontrollers. The key contributions of this work are threefold. The use of two microcontrollers with improved characteristics, such as speed and memory, for faster and more accurate computations significantly improves upon previous systems. Also, for the first time, an active memristor is used in a discrete-time system, which is implemented by using a microcontroller. Furthermore, the system is compared with two different types of microcontrollers regarding the execution time and the quality of the produced bifurcation diagrams. The proposed memristive cubic map uses computationally efficient polynomial functions, which are well suited to microcontroller-based systems, in contrast to more resource-intensive trigonometric and exponential functions. Bifurcation diagrams and a Lyapunov exponent analysis from simulating the system in Mathematica revealed hyperchaotic behavior, along with other significant dynamical phenomena, such as regular orbits, chaotic trajectories, and transitions to chaos through mechanisms like period doubling and crisis phenomena. Experimental verification confirmed the consistency of the results across microcontroller platforms, underscoring the practicality and potential applications of active memristor-based chaotic systems. [ABSTRACT FROM AUTHOR]

The isolated boost full-bridge converter (IBFBC) is a DC–DC conversion topology that achieves a high boost ratio and provides electrical isolation, making it suitable for applications requiring both. Its operational dynamics are often intricate due to its inherent characteristics and the prevalent usage of nonlinear switching elements, leading to bifurcation and chaos. Chaos theory was employed to investigate the impact of changes in the voltage feedback coefficient K and input voltage E on the dynamic behavior of the IBFBC when operating in discontinuous conduction mode (DCM). Based on an analysis of its operating principles, a discrete iterative mapping model of the system in DCM is constructed using the stroboscopic mapping method. The effects of two control parameters, namely the proportional coefficient and input voltage, on system performance are studied using bifurcation diagrams, fold diagrams, Poincaré sections, and Lyapunov exponents. Simulation experiments are conducted using time-domain and waveform diagrams to validate the discrete mapping model and confirm the correctness of the theoretical analysis. The results indicate that when the IBFBC operates in DCM, its operating state is influenced by the voltage feedback coefficient K and input voltage E . Under varying values of K and E , the system may operate in a single-period stable state, multi-period bifurcation, or chaotic state, exhibiting typical nonlinear behavior. [ABSTRACT FROM AUTHOR]

Initial condition-related coexisting behavior is one of the significant features of specific chaotic systems, which corresponds to the complicated coexistences of multiple attractors or infinite attractors. To modulate the three outputs of the Chua's system to generate infinite attractors, this paper proposes a state-extension approach via introducing the three outputs to extra dimensions through a simple integral without or with self-feedback. In comparison with most existing initial condition-controlled offset-boostable systems with discontinuous step-boost-type coexisting attractors, this approach has two important features, i.e., the seed Chua's system is kept unchanged, and infinite continuous offset-boosted attractors or infinite continuous space-scaled attractors can be generated via configuring different initial conditions of the extra introduced variables. Both numerical study and circuit simulation confirmed the feasibility of the design. [ABSTRACT FROM AUTHOR]

The Ueda oscillator is one of the most popular and studied nonlinear oscillators. Whenever subjected to external periodic excitation, it exhibits a fascinating array of nonlinear behaviors, including chaos. This research introduces a novel fractional discrete Ueda system based on Y -th Caputo fractional difference and thoroughly investigates its chaotic dynamics via commensurate and incommensurate orders. Applying numerical methods like maximum Lyapunov exponent spectra, bifurcation plots, and phase plane. We demonstrate the emergence of chaotic attractors influenced by fractional orders and system parameters. Advanced complexity measures, including approximation entropy ( A p E n ) and C 0 complexity, are applied to validate and measure the nonlinear and chaotic nature of the system; the results indicate a high level of complexity. Furthermore, we propose a control scheme to stabilize and synchronize the introduced Ueda map, ensuring the convergence of trajectories to desired states. MATLAB R2024a simulations are employed to confirm the theoretical findings, highlighting the robustness of our results and paving the way for future works. [ABSTRACT FROM AUTHOR]

Numerous studies on the number pi (π) explore its properties, including normality and applicability. This research, grounded in two hypotheses, proposes and proves a theorem that employs a Bernoulli experiment to demonstrate the high probability of encountering any finite bit string within a sequence of consecutive bits in the decimal part of π. This aligns with findings related to its normality. To support the hypotheses, we present experimental evidence about the equiprobable and independent properties of bits of π , analyzing their distribution, and measuring correlations between bit strings. Additionally, from a cryptographic perspective, we evaluate the chaotic properties of two images generated using bits of π. These properties are evaluated similarly to those of encrypted images, using measures of correlation and entropy, along with two hypothesis tests to confirm the uniform distribution of bits and the absence of periodic patterns. Unlike previous works that solely examine the presence of sequences, this study provides, as a corollary, a formula to calculate an upper bound N. This bound represents the length of the sequence from π required to ensure the location of any n-bit string at least once, with an adjustable probability p that can be set arbitrarily close to one. To validate the formula, we identify sequences of up to n = 40 consecutive zeros and ones within the first N bits of π. This work has potential applications in Cryptography that use the number π for random sequence generation, offering insights into the number of bits of π required to ensure good randomness properties. [ABSTRACT FROM AUTHOR]

Summary: Wireless sensor networks (WSN) are innately resource restrained and beneficial in a wide range of applications, including smart homes, e‐health care, law, military systems, disaster management, and emergency reprieve. These applications are linked to various devices that may communicate with one another through the internet, typically known as Internet of Things (IoT). The application of WSN plays an integral role in the IoT infrastructure. In a WSN, sensors are haphazardly placed in environments where the data transmission is challenged by privacy concerns. This paper proposes a methodology termed Lie hypergraph and chaos‐based secure routing (LH‐CSR) to perform an energy‐efficient routing with secure data transmission in WSN. In the first phase, the deployed sensor nodes are transformed into a hypergraph from which cluster head (CH) is elected by hypergraph transversal property, and for secure routing, the route is formed by the Lie commutators of the Lie algebra of upper triangular matrices. The second phase emphasizes privacy preservation by introducing the novel chaotic map formulation to process the key generation. The encryption and decryption processes are maintained by key generation to prevent data loss during retrieval. In this way, the data are retained confidentially with minimal computational overhead. The performance of the LH‐CSR is evaluated through a simulation, which shows that it outperforms over compared protocols in terms of cryptographic time, network lifetime, packet delivery ratio, end‐to‐end delay, and throughput. [ABSTRACT FROM AUTHOR]

Purpose: Tumor-induced angiogenesis is a dangerous state of the tumor growth process in which solid tumors have a blood supply. Modeling has been a very important tool in studying tumor growth and angiogenesis. In this paper, we developed a cancer model by introducing tumor angiogenesis agents to better highlight the role of these chemical substances in tumor-induced vascularization. Our model can reconstruct the transition from a pre-angiogenic to a post-angiogenic state. Materials and Methods: The proposed model comprises five variables: host cells (normal cells), immune cells, tumor cells, endothelial cells, and tumor angiogenesis agents. Chaotic behavior in the production of different populations of cells during vascular growth may confer survival advantages to tumors. Our model has a chaotic regime, which is an indication of tumor-induced angiogenesis dynamics. The fixed points are analyzed biologically, and stability analysis is performed via their eigenvalues. We analyzed the model dynamics via observability and bifurcation analysis. Results: The numerical simulations illustrate biological and clinical findings about vascular tumors. The results show that the proposed model with the existence of tumor angiogenesis agents could capture both avascular and vascular stages of tumor growth. There is no effect of tumor cell killing rate via immune cells on the system dynamics. However, the increase of inhibitory factors of tumor angiogenesis agents leads to the termination of chaos. Conclusion: Our results show the ineffectiveness of targeted treatments on the immune system, which has been confirmed by many negative treatment methods in immunotherapies. Tumor-secreted inhibitor factors are essential to regulating the angiogenesis process. However, increasing inhibitor factors via anti-angiogenic drugs would be a more effective therapeutic approach to eradicate metastasis. [ABSTRACT FROM AUTHOR]

At present, design and applications of discrete chaotic systems aroused much interests of scholars. A practical way to design new chaotic systems is based on existing classical systems. In this paper, based on the existing Hénon map, a class of new Hénon maps are proposed and investigated. Furthermore, the dynamic characteristics of a chosen map are analyzed by numerical simulations including phase diagrams, bifurcation diagrams and Lyapunov exponents. It shows that the system has rich dynamical behaviors. An analogue circuit of the new system is designed and its real hardware circuit is realized. The experiment demonstrates the succuss of the design. Finally, an application in the design of welded beams is carried out using the golden Jackal optimization algorithm which is improved based on the randomness and ergodicity of the generated chaos. The potential practical application based on the proposed system in the engineering field is demonstrated. [ABSTRACT FROM AUTHOR]

A thermal tooth backlash model of a planetary gear system, which includes the effects of thermal deformation and thermal elastohydrodynamic lubrication film, was established. The variation laws of tooth backlash under variable speed, variable torque, and constant power conditions, as well as the nonlinear dynamic characteristics of the system were analyzed. The results showed that the change in tooth backlash is greatly influenced by thermal deformation numerically, while the thermal elastohydrodynamic lubrication film affects the trend of tooth backlash along the meshing line direction. Combining bifurcation diagrams, Largest Lyapunov exponent plots, poincaré sections, phase portraits, and frequency spectra analysis reveals that under variable speed and constant power conditions, the presence of thermal tooth backlash reduces the chaotic range of the system and transforms some unstable motion states into more stable ones. However, for variable torque conditions, the influence of thermal tooth backlash on the system is more complex with both stable and unstable situations coexisting. This study provides a theoretical basis for selecting backlash parameters in planetary gear system design and avoiding chaotic responses. [ABSTRACT FROM AUTHOR]

The herd behavior of prey plays an important role in the predator–prey system. In this paper, we analyze the dynamical properties of a discrete predator–prey model with herd behavior. We found that due to the introduction of herd effects, this model exhibits complex dynamical behavior such as codimension-1 bifurcation (Flip and Neimark–Sacker bifurcations) and codimension-2 bifurcation (1:2, 1:3, and 1:4 strong resonance). Using the center manifold theorem and normal form theory, we obtained the critical conditions that may lead to changes in the stability of the system and even the emergence of new stable states or oscillating behaviors. Numerical simulations not only validate theoretical proofs but also reveal the complex and rich dynamical behavior of the discrete model. [ABSTRACT FROM AUTHOR]

The main objective of this study is to investigate the chaotic dynamics and analog circuit implementation of a nonautonomous single inertial neuron. First, the dimensionless mathematical model of such neuron is established. The equilibria with three kinds of stabilities are then depicted, and system symmetry and Hamilton energy function are analyzed, respectively. In numerical simulations, by using the two-dimensional/one-dimensional bifurcation diagrams, Lyapunov exponent spectra, phase plots, and basins of attraction, bifurcation of coexisting bubbles as well as bi-stable patterns are revealed, where the generated coexisting attractors are symmetric about the origin. In addition, we confirm that the complexity of the basins of attraction deteriorates with the increase of the frequency parameter. Finally, analog circuit experiments with few analog circuit elements are deployed, via which the bi-stable patterns of the model are well verified. [ABSTRACT FROM AUTHOR]

This paper provides a solution to the new fractional-order Lorenz–Stenflo model using the adaptive predictor–corrector approach and the ρ -Laplace New Iterative Method ( L ρ N I M ), representing an extensive comparison between both techniques with RK4 related to accuracy and error analysis. The results show that the suggested approaches allow one to be more accurate in analyzing the dynamics of the system. These techniques also produce results that are comparable to the results of other approximate techniques. The techniques can, thus, be used on a wider class of systems in order to provide more accurate results. These techniques also appropriately identify chaotic attractors in the system. These techniques can be applied to solve various numerical problems arising in science and engineering in the future. [ABSTRACT FROM AUTHOR]

In this work, we employ simulations to investigate deterministic and stochastic dynamics of a system governed by four coupled nonlinear ordinary differential equations (ODEs) derived from the canonical three-dimensional Chua model, replacing the piecewise nonlinearity with a cubic function. We employed two simulation approaches: (i) using software — where we performed numerical simulations (digital computation) in the ODEs model, and (ii) using hardware — where we performed experimental studies (analog computation) in the ODEs model. In the initial software-based approach for simulations, we performed stability and bifurcation analyses of the trivial equilibrium point, which were analytically conducted, along with the numerical continuation method. We solved the model using digital computation and explored its intricate dynamical behavior through nonlinear dynamics techniques applied to the parameter planes. In the second approach, employing hardware for simulations through analog computation, we designed an electronic circuit using analog electronics to solve the model in a continuous-time integration. The experimental setup mirrored the numerical simulations, yielding comparable results in terms of dynamical behaviors. This study underscores significant agreement between numerical and experimental findings, highlighting the robustness of the model across digital and analog contexts and offering practical insights into the various nonlinear dynamics presented in this system. [ABSTRACT FROM AUTHOR]

Memristives provide a high degree of non-linearity to the model. This property has led to many studies focusing on developing memristive models to provide more non-linearity. This article studies a novel fractional discrete memristive system with incommensurate orders using ϑ i -th Caputo-like operator. Bifurcation, phase portraits and the computation of the maximum Lyapunov Exponent (L E m a x) are used to demonstrate their impact on the system's dynamics. Furthermore, we employ the sample entropy approach (SampEn), C 0 complexity and the 0-1 test to quantify complexity and validate chaos in the incommensurate system. Studies indicate that the discrete memristive system with incommensurate fractional orders manifests diverse dynamical behaviors, including hidden chaos, symmetry, and asymmetry attractors, which are influenced by the incommensurate derivative values. Moreover, a 2D non-linear controller is presented to stabilize and synchronize the novel system. The work results are provided by numerical simulation obtained using MATLAB R2024a codes. [ABSTRACT FROM AUTHOR]

In this paper, a class of discrete-time predator–prey system with fear factor and harvesting effect is proposed, and its complex dynamic behavior is analyzed. First, the existence and stability of equilibrium points of the discrete system are studied. Second, the critical value expressions of Neimark–Sacker bifurcation and flip bifurcation are obtained by bifurcation theory. Third, we control the bifurcation and chaos of the system by using feedback control strategies. The optimal harvesting strategy is obtained by using the Pontryagin maximum principle. Finally, we use MATLAB software to carry out some numerical simulations, which not only verify our theoretical results, but also analyze the rich dynamic behavior of the system. [ABSTRACT FROM AUTHOR]

This paper introduces an efficient, lightweight, invisible, blind, real-time video watermarking system. Symmetric chaotic key encryption enhances the system’s security, ensuring robustness by randomly selecting pixels or coefficients for watermark embedding. The first-level discrete wavelet transform (DWT) is applied to selected data, embedding the watermark into the low-frequency band (LL sub-band). The approach involves random selection of data for quantization using the quantization index modulation (QIM) technique. The proposed scheme is implemented on a low-cost FPGA board (Zybo Z7-20), using a software/hardware (SW/HW) co-design approach. Experimental results demonstrate high fidelity with a peak signal-to-noise ratio (PSNR) exceeding 35 dB and normalized correlation (NC) around 0.99. The architecture achieves a balanced compromise between low FPGA area with high operational speed up to 127 MHz and minimal power consumption not exceeding 51 mW. Performance evaluation confirms the system’s robustness against various attacks, including filtering, additional noise, geometrical modifications, and contrast adjustments. This makes it highly suitable for real-time embedded video applications where data integrity is paramount. [ABSTRACT FROM AUTHOR]

To investigate the mechanical properties and nonlinear energy evolution mechanism of holed limestone, triaxial compression tests under hydro-mechanical coupling were conducted on holed limestones with varying hole numbers. Based on nonlinear dynamics and rock micro-energy evolution theory, the chaotic characteristics of the energy evolution process were explored. The results show that under the action of hydro-mechanical coupling, the peak strength and residual strength of the holed limestone increase with the increase of confining pressure, and the maximum increase ratios are 25.17% and 89.33%, respectively. With the increase of hole numbers and pore pressure, the maximum decreases are 22.32%, 46.07% and 17.39%, 52.81%, respectively. The deformation and failure process of holed limestone can be divided into the following five stages: nonlinear oscillation, nonlinear transcritical stability weakening, nonlinear stability, period-doubling bifurcation before chaos, and the chaotic stage. When stress reaches 81% of the peak stress, the crack periodically expands in the rock, and as it reaches 83%, the crack irregularly expands in the rock. When the energy growth factor r is 3 and 3.57, the corresponding periodic crack propagation stress σ pcg and chaotic initial stress σ cis can be considered as crack initiation stress and crack damage stress, which provides a new method for determining crack initiation stress and crack damage stress. The periodic crack propagation stress (representing crack initiation stress) and chaotic initial stress (indicating crack damage stress) of holed rocks gradually decrease with the increase in hole number and pore pressure, and gradually increase with the increase in confining pressure. Highlights: A triaxial specimen model was established based on karst fracture-pipe erosion. The effects of confining pressure, pore pressure, and hole number on the strength of holed limestone under hydro-mechanical coupling were investigated Two new nonlinear indexes are defined based on the relationship between the r value and stress increment It provides a new method for determining crack initiation stress and crack damage stress [ABSTRACT FROM AUTHOR]

This research study involves modeling Newton–Leipnik attractors within the domain of fractional variable-order (FVO) dynamics using a nonlinear and adaptable radial basis function neural network (RBFNN). The numerical solution for the FVO Newton–Leipnik system is initially obtained using a numerical scheme based on the Caputo–Fabrizio derivative with variable order. This process is carried out across a range of different control parameters. A parametric model is also constructed using RBFNN, considering various system initial values. Multiple instances of chaos are calculated using a proposed computational model within the Newton–Leipnik system with varying fractional-order functions. This investigation aims to assess and comprehend the extent of sensitivity exhibited by chaotic behavior achieved through the computation of Lyapunov exponents. The performance of the proposed computational RBFNN model is validated using the RMSE statistic. The results closely align with those obtained through numerical algorithms based on the Caputo–Fabrizio derivative, demonstrating the high accuracy of the designed network. [ABSTRACT FROM AUTHOR]

In the era of digitization and informatization, 3D models are used in a variety of fields, notably in medicine, engineering and design, seamlessly integrating into people's daily lives. Particularly within the medical field, 3D models enjoy extensive utilization. Consequently, this paper introduces a novel 3D medical model encryption algorithm, designated as 3D3A-SMA. First, a five-dimensional hyperchaotic system with multiple stability is applied to the encryption process of this algorithm. In this encryption algorithm, the vertex data of the 3D model is divided into integer and fractional parts and different diffusion methods are applied to them, respectively. A 3D Arnold spiral subregion diffusion based on chaotic system (3ASDC) is proposed to diffuse the integer part, and then, a selectable multiple spiral arrangement subregion diffusion (SMASD) is proposed to diffuse the fractional part. The simulation results and performance analysis show that the proposed encryption algorithm can accurately encrypt and decrypt the 3D medical model. The numerical results in the performance analysis are very close to the ideal values, with the information entropy of the ciphertext and each dimension reaching 7.998. In addition, the correlation within the ciphertext is also very close to the ideal value of 0.000, The algorithm also shows strong resistance to common attacks. [ABSTRACT FROM AUTHOR]

A underlying complex dynamical behavior of double Allee effects in predator-prey system is studied in this article to understand the predator-prey relation more intensely from different aspects. We first propose a system with the Caputo sense fractional-order predator-prey system incorporating the Allee effect in prey populations to explain how the memory effect can change the different emergent states. Local stability analysis is analyzed by applying Matignon’s condition for the FDE system. Further, we consider a discrete-time system to show the influence of double Allee effects in non-overlapping generations. For discrete-time system, different bifurcations like Neimark-Sacker, flip bifurcations, irregularity in periodic oscillations, are observed. Irregularity occurs through a period-doubling cascade which is a common route to chaos in a dynamical sense. Maximum Lyapunov exponent (MLE) is shown to illustrate the irregular behaviors of discrete-time systems. The Allee effect influences system stability where the strong Allee effect enhances system stability whereas the stability is lost for the weak Allee effect. The extinction risk of populations in the presence of the Allee effect is a concerning issue. We have insight into how all populations survive along with stable extinction equilibrium. Our proposed systems exhibit different alternative states. Multiple stable attractor basins are plotted to depict the different alternative states of the FDE system as well as the discrete-time system. Initial population densities play a key role in the coexistence of all the populations otherwise there is a risk of species extinction. Besides analytical results, numerical simulation is performed to valid our analytical findings of different dynamical states like bifurcation, stability, irregularity as well as multi-stability. [ABSTRACT FROM AUTHOR]

The paper proposes a method for solving the problem of synthesis of an adaptive control system for unstable and deterministic chaotic processes in the class of 'dovetail' catastrophes for objects with m-inputs and n-outputs. The synthesis problem is solved by the gradient-velocity method of Lyapunov vector functions. From the conditions of the aperiodic robust stability of the etalon model with the desired dynamics of the main control loop and the generalised configurable object, the control goal is achieved. One of the most promising ways of solving the problem of managing unstable and deterministic chaotic processes is the synthesis of a control system in the class of 'swallowtail' catastrophes and the use of adaptation methods. Selecting and studying a reference model, and employing the gradient-velocity method for a generalised configurable control object ensure robust stability, utilise current information effectively, and achieve desired system quality and management goals. [ABSTRACT FROM AUTHOR]

Elementary Cellular Automata (ECA) are well-studied computational universes capable of impressive computational variety, but harnessing their potential has been challenging. When combined with Reservoir Computing (RC), harnessing this computation becomes feasible, and furthermore enables energy efficient AI. This study compares ECA reservoirs to topological heterogeneous and more biological plausible counterparts of Partially-Local CA (PLCA) and Homogeneous Homogeneous Random Boolean Networks (HHRBN). Using the 5-bit memory benchmark, Temporal Derrida plots and collapse rate, finding are that more disordered topology does not equate to more disordered computation and moreover the evidence suggest this heterogeneity shrinks the critical range. [ABSTRACT FROM AUTHOR]

In sport, as in life, people experience transitions on a regular basis. This exploratory research examined the experience of the transitional process within sport using a qualitative methodology. The seven participants had worked within their sport for over 30 years, first as an athlete, then a coach, and finally a coach developer. Semistructured interviews with each participant (x2) allowed for exploration of their experiences of changing roles within their organizations and revealed three themes: importance of timely support, ongoing professional conversations, and where am I going with this? These themes, exemplified by the use of direct quotes from the participants, were used to provide context and deeper understanding of the transition from athlete to coach to coach developer. The participants revealed a certain degree of serendipity, due to a lack of structure and process in their experiences. As a result, we suggest some practical steps that organizations could adopt to assist in this process. [ABSTRACT FROM AUTHOR]

Fractional calculus (or arbitrary order calculus) refers to the integration and derivative operators of an order different than one and was developed in 1695. They have been widely used to study dynamical systems, especially chaotic systems, as the use of arbitrary-order operators broke the milestone of restricting autonomous continuous systems of order three to obtain chaotic behavior and triggered the study of fractional chaotic systems. In this paper, we study the chaotic behavior in fractional systems in more detail and characterize the geometric variations that the dynamics of the system undergo when using arbitrary-order operators by asking the following question: is the Lyapunov exponent sufficient to describe the dynamical variations in a chaotic system of fractional order? By quantifying the convex envelope generated by the 2D projection of the system into all its phase portraits, the changes in the area of the system, as well as the volume of the attractor, are characterized. The results are compared with standard metrics for the study of chaotic systems, such as the Kaplan–Yorke dimension and the fractal dimension, and we also evaluate the frequency fluctuations in the dynamical response. It is found that our methodology can better describe the changes occurring in the systems, while the traditional dimensions are limited to confirming chaotic behaviors; meanwhile, the frequency spectrum hardly changes. The results deepen the study of fractional-order chaotic systems, contribute to understanding the implications and effects observed in the dynamics of the systems, and provide a reference framework for decision-making when using arbitrary-order operators to model dynamical systems. [ABSTRACT FROM AUTHOR]

Chaotic states of abnormal vasospasms in blood vessels make heart patients more prone to severe infections of COVID-19, eventually leading to high fatalities. To understand the inherent dynamics of such abrupt vasospasms, an N-type blood vessel model (NBVM) subjected to uncertainties is derived in this paper and investigated both in integer order (IO) as well as fractional-order (FO) dynamics. Active-adaptive controllers are designed to synchronize the chaotic turbulence responsible for undesirable fluctuations in diameter and pressure variations of the blood vessel. The FO-NBVM reveals insightful rich dynamics and faster adaptive synchronization compared to its IO model. The practical implications of this work will be useful in analysing chaotic dysfunctionalities of the blood vessel such as vasoconstriction, ischaemia, necrosis, etc. and help in developing control strategies and modular responses for COVID-19 triggered heart diseases. [ABSTRACT FROM AUTHOR]

The complex dynamics observed in the financial system are key issues in the economic and social fields. Time delays also exist in lots of financial services and have some marked effects on the economy. Therefore, it is significant to study the intricate and abundant dynamical behaviors of a financial system with delays. In this paper, rich dynamics such as quasi-periodic, phase-locked and chaotic solutions, are worth to paying more attention to utilizing results of the time-delayed financial system to avoid disorder in the financial community. Firstly, double Hopf bifurcation points of the equilibrium are obtained by using DDE-BIFTOOL to draw critical curves of Hopf bifurcation. Furthermore, the method of multiple scales (MMS), a powerful analysis tool, is employed to derive the normal form, enabling their unfolding and classification. Two kinds of double Hopf bifurcation have been found. Finally, there are plentiful dynamical behaviors found in this system, such as quasi-periodic, phase locked and chaotic solutions, as well as bistability where two co-existing periodic solutions with different frequencies and amplitudes occur. It is worth mentioning that this paper presents two types of routes to chaos: torus breakdown and period-doubling bifurcation routes to chaos. Bifurcation diagrams and recurrent plots serve as tools for identifying quasi-periodic, phase-locked, and chaotic solutions within the system. These intricate dynamical phenomena offer valuable insights for researchers seeking a deeper understanding of the system’s underlying mechanisms. For achieving optimal performance in the financial system, it becomes imperative to carefully select appropriate delay values. [ABSTRACT FROM AUTHOR]

Purpose: To explore the impact of gear floating on the system's nonlinear dynamic characteristics, a gear floating model was developed based on the concept of gear floating. Methods: A nonlinear dynamic model, bending-torsional-axial-pendular (BTAP), has been developed for a coaxial reverse closed differential herringbone gear transmission system (CRCDHGTS), accounting for gear floating. This model considers factors such as gear floating backlash, tooth surface friction, gyroscopic effects, time-varying meshing stiffness (TVMS), meshing damping, and dynamic meshing parameters. A calculation model for the floating backlash and floating TVMS of a herringbone gear system was derived, and the nonlinear dynamic response of the gear system was solved using the Runge–Kutta method. Results: The influence of input speed, initial backlash, gear float value, and system transmission error on the nonlinear dynamic vibration characteristics is analyzed using various diagrams, including bifurcation diagrams, maximum Lyapunov exponent (MLE) plots, time history diagrams, frequency diagrams, phase diagrams, and Poincaré section diagrams. Conclusions: The research reveals that gear floating diminishes the chaotic motion behavior of the system under different excitation factors, thereby improving the system's global bifurcation characteristics. The developed BTAP coupled nonlinear dynamic model provides more accurate numerical solutions compared to models with fixed meshing parameters, rendering it more suitable for analyzing the system's dynamic characteristics. Analysis of the gear floating value indicates an optimal range of 0–20 μm and 34–43 μm for generating periodic motion, with floating values around 10–20 μm demonstrating better performance in mitigating the negative effects of initial backlash and transmission error. [ABSTRACT FROM AUTHOR]

The relative structural simplicity of chaotic oscillators and the possibility of obtaining signals with a large dimension is of great interest for wireless data transmission and processing. The diversity of signal waveforms from the same source of chaos is provided by a fundamental property of chaotic oscillations: sensitivity to the choice of initial conditions. In this paper, this sensitivity is employed in the proposed method for forming analog chaotic radio pulses of arbitrary (specified) duration using an analog oscillator in such a way that the pulse shape can be changed and repeated from pulse to pulse. To repeat the shape of oscillations for an arbitrarily long period of time is not a problem for digital chaotic oscillators, but for analog systems, this is a challenge due to the impossibility of controlling the initial conditions and the evolution of the analog trajectory. In this paper, a new method for generating chaos is proposed, which can both change and repeat the shape of a chaotic signal of arbitrary duration, i.e., long chaotic radio pulses. The generator acts as a reservoir and as a replicator from which, under external influence, a signal of a certain shape can be extracted, and this shape can be reproduced. The term "long" in this case means that the duration of chaotic radio pulses is many times greater than the characteristic time of divergence of chaotic trajectories. To prove the correctness of the proposed generation method, the results of its experimental implementation in the frequency range of 100 to 500 MHz are given. Examples of forming equal pulses with a duration of about 20 to 200 quasi-periods of oscillations (up to 500 ns) are given. The proposed method provides the technical possibility of forming pulses whose dimensions can vary in a wide range, which is important for implementing large processing gains in various wireless applications. The method can be implemented in various frequency ranges in the class of analog generators of chaotic oscillations, since the employed generation method, i.e., modulation of a transistor generator by supply voltage, is natural for radio engineering. [ABSTRACT FROM AUTHOR]

Host–parasitoid systems are an essential area of research in ecology and evolutionary biology due to their widespread occurrence in nature and significant impact on species evolution, population dynamics, and ecosystem stability. In such systems, the host is the organism being attacked by the parasitoid, while the parasitoid depends on the host to complete its life cycle. This paper investigates the effect of parasitoid aggregation attacks on a host in a host–parasitoid model with self-diffusion on two-dimensional coupled map lattices. We assume that in the simulation of biological populations on a plane, the interactions between individuals follow periodic boundary conditions. The primary objective is to analyze the complex dynamics of the host–parasitoid interaction model induced by an aggregation effect and diffusion in a discrete setting. Using the aggregation coefficient k as the bifurcating parameter and applying central manifold and normal form analysis, it has been shown that the system is capable of Neimark–Sacker and flip bifurcations even without diffusion. Furthermore, with the influence of diffusion, the system exhibits pure Turing instability, Neimark–Sacker–Turing instability, and Flip–Turing instability. The numerical simulation section explores the path from bifurcation to chaos through calculations of the maximum Lyapunov exponent and the construction of a bifurcation diagram. The interconversion between different Turing instabilities is simulated by adjusting the timestep and self-diffusion coefficient values, which is based on pattern dynamics in ecological modeling. This contributes to a deeper understanding of the dynamic behaviors driven by aggregation effects in the host–parasitoid model. [ABSTRACT FROM AUTHOR]

Nonlinear equations are essential in research and engineering because they simulate complicated processes such as fluid dynamics, chemical reactions, and population growth. The development of advanced methods to address them becomes essential for scientific and applied research enhancements, as their resolution influences innovations by aiding in the proper prediction or optimization of the system. In this research, we develop a novel biparametric family of inverse parallel techniques designed to improve stability and accelerate convergence in parallel iterative algorithm. Bifurcation and chaos theory were used to find the best parameter regions that increase the parallel method's effectiveness and stability. Our newly developed biparametric family of parallel techniques is more computationally efficient than current approaches, as evidenced by significant reductions in the number of iterations and basic operations each iterations step for solving nonlinear equations. Engineering applications examined with rough beginning data demonstrate high accuracy and superior convergence compared to existing classical parallel schemes. Analysis of global convergence further shows that the proposed methods outperform current methods in terms of error control, computational time, percentage convergence, number of basic operations per iteration, and computational order. These findings indicate broad usage potential in engineering and scientific computation. [ABSTRACT FROM AUTHOR]

In a recent paper [Belykh et al., 2024], we proved that the bifurcation structure of a quadratic noninvertible map persists when the parameter increases from zero and the map turns into an invertible multidimensional Henon map. In this paper, we consider a similar problem for a generalized map which combines the Henon-type maps, the Poincaré return map for Shilnikov bifurcation of saddle-focus homoclinic orbit, the Lurie discrete time system, etc. We have obtained the expected result about the persistence of periodic orbits and their bifurcations when passing from a One-Dimensional (1D) endomorphism to the generalized map as a small parameter becomes nonzero. We have revealed the precise mechanism of change of homoclinic orbits and splitting of unstable manifolds as a result of the transition of 1D endomorphism to multidimensional map. Thereby we have derived the reconstruction rules of nonwandering set of orbits and bifurcations of the generalized map from those of 1D endomorphism. [ABSTRACT FROM AUTHOR]

Chaos in a DC–DC boost converter operating in discontinuous conduction mode when controlled by sliding mode control is detected. A route to chaos through sliding bifurcations is shown along with the coexistence of the chaotic regime with a stable operating point. A bifurcation analysis in the sliding vector field is carried out with the objective of defining a range of values for which control parameters guarantee the robustness of the system, at least locally. The analysis is based on the study of possible sliding bifurcations, that is, bifurcations inherent to the sliding dynamics. It is rigorously shown that there is an unstable limit cycle in the sliding dynamics due to a subcritical Hopf bifurcation. The existence of this limit cycle and its evolution with parameters turn out to be of great importance for the stability and robust control of this type of power converter. [ABSTRACT FROM AUTHOR]

A control strategy combining cubic displacement feedback nonlinear control and proportional-differential (PD) linear control is used to control the vibration performance of the maglev system. The maglev system is divided into positive stiffness maglev system, quasi-zero stiffness maglev system and negative stiffness maglev system according to the linear stiffness value of maglev system. Firstly, an improved multi-scale method is used to analyze the vibration characteristics of suspension in the positive stiffness state of the maglev system. Secondly, the influence of control parameters on train vibration amplitude and vibration center displacement under quasi-zero stiffness is studied. Finally, the vibration characteristics of the train when the maglev system is in negative stiffness are analyzed by numerical simulation. The maglev system exhibits the worst vibration performance under negative stiffness compared with positive stiffness and quasi-zero stiffness. The suspension frame is easy to enter the chaotic motion state, and its vibration center is easy to deviate from the equilibrium position and produce large displacement when the maglev system is in the negative stiffness state. The control results show that the control strategy combining the cubic displacement feedback nonlinear control with the PD linear control can make the maglev system exhibit better vibration characteristics under positive and quasi-zero stiffness. [ABSTRACT FROM AUTHOR]