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In recent decades, impulse control has been increasingly applied as a discontinuous control method across diverse domains such as satellite orbit transfers, financial market regulation, chaos synchronization, and communication security. This paper investigates an impulse synchronization strategy specifically tailored for chaotic financial systems. We propose a novel strategy grounded in Lyapunov stability theory and the maximum Lyapunov exponent, designed to synchronize chaotic financial systems effectively. Simulation experiments are conducted to validate the efficacy of our proposed approach. [ABSTRACT FROM AUTHOR]

Phenomenon of cluster synchronization has captured the curiosity of scientists in the study of nonlinear dynamics over the last few decades. It is a well-known and intriguing aspect of complex systems that has garnered significant attention in research. Many researchers have significantly addressed the synchronization of cluster-based networks with identical and non-identical systems in the literature. This review paper presents a detailed summary of overall developments in the domain of cluster synchronization of chaotic system networks. After introducing the chaotic systems and concept of cluster synchronization initially; the applicability of synchronization in several fields including secure communication, information processing, and the synchronization of complex networks, has been highlighted in the later part of the paper. In general, for meeting out the goal of cluster synchronization, several strategies including standard Lyapunov design- based approach, pinning control, observer-based control, time-delayed feedback control, adaptive synchronization etc. are prominently used in literature. The article briefly discusses these approaches and reviews their advantages and disadvantages along with some possible applications. The overarching goal of this literature review is to provide a comprehensive summary of current research on cluster synchronization in chaotic systems and to point the way toward promising avenues for further investigation. The overarching goal of this literature review is to provide a comprehensive summary of current research on cluster synchronization in chaotic systems and to point the way toward promising avenues for further investigation. [ABSTRACT FROM AUTHOR]

This paper focuses on synchronization control of the fractional-order unified chaotic system. First, the stability of equilibria is analyzed by the Routh–Hurwitz criteria. Then, three different controllers are designed to achieve chaos synchronization of the drive-response unified system. Further, the impact of the fractional order on the synchronization performance is illustrated. Numerical simulations are carried out to verify the feasibility of theoretical analysis. [ABSTRACT FROM AUTHOR]

Beyond 5G networks provide solutions for next-generation communications, especially digital twins networks (DTNs) have gained increasing popularity for bridging physical and digital space. However, current DTNs pose some challenges, especially when applied to scenarios that require efficient and multimodal data processing. Firstly, current DTNs are limited in communication and computational efficiency, since they require to transmit large amounts of raw data collected from physical sensors, as well as to ensure model synchronization through high-frequency computation. Second, current models of DTNs are domain-specific (e.g. E-health), making it difficult to handle DT scenarios with multimodal data processing requirements. Finally, current security schemes for DTNs introduce additional overheads that impair the efficiency. Against the above challenges, we propose a large language model (LLM) empowered DTNs framework, LLM-Twin. First, based on LLM, we propose digital twin semantic networks (DTSNs), which enable more efficient communication and computation. Second, we design a mini-giant model collaboration scheme, which enables efficient deployment of LLM in DTNs and is adapted to handle multimodal data. Then, we designed a native security policy for LLM-twin without compromising efficiency. Numerical experiments and case studies demonstrate the feasibility of LLM-Twin. To our knowledge, this is the first to propose an LLM-based semantic-level DTNs. [ABSTRACT FROM AUTHOR]

Variational modal decomposition (VMD) has proven to be an effective technique for improving the accuracy of runoff prediction and has been widely used in runoff analysis and prediction. However, the presence of noise and outliers can complicate the runoff decomposition, so obtaining purely stochastic and deterministic components is difficult. Therefore, exploring the chaotic properties of the components obtained from decomposition can provide a new perspective to reveal intrinsic variability patterns and enhance our understanding of the unity of determinism and stochasticity. In this study, a two-stage VMD framework is proposed to decompose the monthly runoff, with the chaotic characteristics analyzed by employing an unthreshold recurrence plot and the largest Lyapunov exponent. Additionally, a chaotic prediction model is developed using phase space reconstruction, Volterra filter, and wavelet neural network methodologies. The model is validated using monthly runoff data from four stations in the Yellow River Basin, China. The results demonstrate that, although the VMD method effectively isolates trend components in monthly runoff, it still exhibits challenges in separating periodic and random elements, leading to the identification of chaotic components characterized by the amalgamation of periodicity and randomness. Notably, the two-stage VMD-phase space reconstruction-Volterra-wavelet neural networks model outperforms the VMD-phase space reconstruction-Volterra-wavelet neural networks model, with a substantial increase in Nash–Sutcliffe efficiency during validation, rising from an average of 0.9271–0.9508 and reaching a maximum of 0.96 across the four stations. Overall, this study demonstrates the potential of VMD for improving the monthly runoff prediction accuracy and elucidates the interplay between determinism and stochasticity in runoff analysis, offering valuable insights for further research in this area. [ABSTRACT FROM AUTHOR]

Irregular and complex behavior in the financial system can disrupt stability and smooth economic growth. It causes randomness within the system, generating chaos; hindering synchronization behaviour. Achieving smooth and rapid synchronization between two coupled hyperchaotic finance (HF) systems with lessened fluctuation of input and output signals is vital for continuing financial stability and fostering economic growth, a challenge addressed in this article. The paper proposes a novel time-efficient nonlinear control (TENLC) technique and investigates HF systems synchronization using the drive-response system (DRS) arrangement. The proposed TENLC strategy realizes fast and smooth synchronization behaviour between two coupled HF systems, reducing closed-loop state-variable trajectory oscillations. The controller is designed to retain the nonlinear components within the closed-loop system and does not depend on the system's parameters, simplifying the design and analysis process. The Lyapunov stability technique confirms the closed-loop's global stability at the origin. Proofs of mathematical analysis and computer-based simulation results validate the theoretical findings, showing that the presented TENLC strategy converges the state error trajectories to zero in a short transient time with lessened fluctuations for all signals. The comparative computer-based simulation analysis confirms that the presented TENLC approach outperforms other synchronization control techniques. [ABSTRACT FROM AUTHOR]

In the application of DNA‐based chaotic synchronization, the precise values of the system parameters are often complicated to attain due to the interference of external factors, thus weakening the performance of synchronization. In this paper, considering the case of unknown parameters in chaotic systems, a method of adaptive synchronization based on DNA strand displacement (DSD) is proposed. Firstly, the chain replacement reaction modules of emergence, activation and degradation are given through the design of DNA strand, which enable the realization of Yang chaotic system using the mass action dynamics law. Further, in order to achieve the estimation of the unknown parameters and the stability of the error system, the rules for identification of unknown parameters are derived and adaptive controllers are designed under the adaptive control principle. Finally, an internal synchronization approach is recommended to decompose the chaotic system into subsystems of different orders, which can freely choose subsystems to complete synchronization. Subsequently, numerical simulations show that DNA‐based adaptive controllers can fulfill the internal synchronization of Yang system with unknown parameters and are robust to parameter deviations. In addition, the strategy presented in this study can be extended to the synchronization control of other DSD‐based multivariable chaotic systems. [ABSTRACT FROM AUTHOR]

The establishment of a financial system should not only consider the current situation, but also need to refer to the past. Due to the memory of the fractional derivative, a fractional-order system can more effectively describe the historical significance of the financial system. Most scholars use the prediction–correction scheme to study fractional-order systems. This paper provides a higher-precision numerical method for the financial system, which more effectively simulate the system. Based on the definition of the Grünwald–Letnikov fractional derivative, the integer-order system with nonconstant demand elasticity is extended to the fractional-order setting, and its dynamic behavior is studied, with some novel chaotic attractors found. The research results are helpful for improving the understanding of the financial system and the financial market and for predicting financial risks. [ABSTRACT FROM AUTHOR]

This work investigates a fractional-order multi-wing chaotic system for detecting weak signals. The influence of the order of fractional calculus on chaotic systems' dynamical behavior is examined using phase diagrams, bifurcation diagrams, and SE complexity diagrams. Then, the principles and methods for determining the frequencies and amplitudes of weak signals are examined utilizing fractional-order multi-wing chaotic systems. The findings indicate that the lowest order at which this kind of fractional-order multi-wing chaotic system appears chaotic is 2.625 at a = 4 , b = 8 , and c = 1 , and that this value decreases as the driving force increases. The four-wing and double-wing change dynamics phenomenon will manifest in a fractional-order chaotic system when the order exceeds the lowest order. This phenomenon can be utilized to detect weak signal amplitudes and frequencies because the system parameters control it. A detection array is built to determine the amplitude using the noise-resistant properties of both four-wing and double-wing chaotic states. Deep learning images are then used to identify the change in the array's wing count, which can be used to determine the test signal's amplitude. When frequencies detection is required, the MUSIC method estimates the frequencies using chaotic synchronization to transform the weak signal's frequencies to the synchronization error's frequencies. This solution adds to the contact between fractional-order calculus and chaos theory. It offers suggestions for practically implementing the chaotic weak signal detection theory in conjunction with deep learning. [ABSTRACT FROM AUTHOR]

Improving neurons in a real physiological environment and studying their electrical behavior is crucial for understanding human cognitive brain functions and neural dynamics. Neuronal cells reside in a complex physiological environment, where the electromagnetic fields generated by ion transmembrane movements affect their discharge activity. Therefore, to better simulate the real conditions of biological neurons, this paper incorporated the characteristics of the memristor and constructed a four-dimensional Morris-Lecar (ML) neuron model by adding a magneto-controlled memristor into the three-dimensional ML neuron model. Through the study of time series diagrams, phase plane diagrams, inter-spike interval (ISI) bifurcation diagrams, we explored the effects of the feedback gain coefficient and the relationship coefficient between membrane potential and magnetic flux on the firing behavior of neurons in the model. It was found that variations in these two parameters can lead to complex firing patterns in neurons. We also utilized the maximum Lyapunov exponent and dissipative theory to investigate the chaotic synchronization phenomenon in the memristor-based ML neuron model. Additionally, we explored the impact of noise on neuronal synchronization behavior within the system, finding that an appropriate noise intensity can effectively accelerate the neurons' attainment of a synchronized state. Finally, applying the chaotic synchronization system to secure Communication, the simulation results and related analysis demonstrate that the system excels in encrypting and decrypting voice signals, offering high levels of security and confidentiality. [ABSTRACT FROM AUTHOR]

This research focuses on a mathematical examination of a path to sliding period doubling and chaotic behaviour for a novel limited discontinuous systems of dimension three separated by a nonlinear hypersurface. The switching system is composed of dissipative subsystems, one of which is a linear systems, and the other is not linked with equilibria. The non-linear sliding surface is designed to improve transient response for these subsystems. A Poincare return map is created that accounts for ´ the existence of the hypersurface, completely describing each individual sliding period-doubling orbits that route to the sliding chaotic attractor. Through a rigorous analysis, we show that the presence of a nonlinear sliding surface and a set of such hidden trajectories leads to novel bifurcation scenarios. The proposed system exhibits period-m orbits as well as chaos, including partially hidden and sliding trajectories. The results are numerically verified through path-following techniques for discontinuous dynamical systems. [ABSTRACT FROM AUTHOR]

This publication investigates the performance of demodulation methods utilized in spread spectrum chaotic communication systems in order to understand conditions at which advanced demodulation methods, such as chaotic synchronization, provide tangible benefits over classical, matched filtering-based approaches. We conduct simulations and comparisons of three different communication systems: classic direct sequence spread spectrum (DSSS), chaotic signal fragment-based pseudo-chaotic spread spectrum (PCSS), and chaotic synchronization-based antipodal chaos shift keying (ACSK). These systems possess similar spectral and time domain characteristics, allowing us to shed light on their fundamental differences and limitations in chaos-based communication. Additionally, we assess the impact of frequency modulation (FM) on these modulation methods, as FM allows the creation of simplified non-coherent modulation schemes. Our findings, based on the analysis of bit error ratio (BER) curves, demonstrate that in the case of a non-dispersive communication channel, the utilization of chaotic synchronization does not allow to achieve performance of correlation-based receivers. Additionally, the utilization of chaotic synchronization for multiple access poses certain challenges due to malicious synchronization between users. As a supplementary finding, we show that in systems with matched filter-based demodulation, discrete-time quantized spreading sequences confer an advantage over analogous, continuous-time spreading waveforms. [ABSTRACT FROM AUTHOR]

In this paper, we propose an analytical approach to estimate the largest Lyapunov exponent (LLE) of a Rössler chaotic system, leveraging the synchronization method. This research focuses on establishing an analytical criterion for the synchronization of two identical Rössler chaotic systems through the linear coupling of state variables. This is crucial because the LLE of such systems can be estimated based on the critical coupling required for synchronization. Unlike previous studies, we first transform the synchronization error system between two identical Rössler chaotic systems into a set of Volterra integral equations by using the Laplace transform and convolution theorem. The critical coupling for synchronization is analytically derived using integral equation theory to solve the error system. As compared to the numerical results of the Rössler chaotic system's LLE, our analytical estimates demonstrate high accuracy. Our findings suggest that the challenge of estimating the Rössler chaotic system's LLE can be simplified to solving a cubic algebraic equation, offering a novel perspective on the analysis of how parameters influence the LLE's value in the Rössler chaotic system.

This study shows, by means of numerical analysis, that the characteristics of discrete dynamical systems, in which chaos and catastrophe coexist, are closely related to the geometric statistics in Finsler geometry. The two geometric statistics introduced are nonlinear connections information, denoted as N I , and the mean deviation curvature, denoted as P ¯. The quantity N I can be used to determine the occurrence of chaos in terms of nonequilibrium stability. The resulting chaos is characterized by P ¯ in terms of the trajectory's robustness, which is related to the localization or globalization of chaos. The characteristics of catastrophe-induced chaos are clearly visualized through the contour topography of N I , in which an abrupt change is represented by cliff topography (i.e. a line of critical points); initial dependence is reflected in the reversibility of topographic patterns. On overlaying the contour topography with the singularity pattern, it is evident that chaos does not arise around the singular point. Furthermore, the extensive development of cusp and butterfly chaos demands information on the nonlinear connections within the singularity pattern. The asymmetry in swallowtail chaos is less distinguishable in an equilibrated state, but becomes more evident when the system is in a state of nonequilibrium. In many analyses, chaos and catastrophe are examined separately. However, these results demonstrate that when both are present, the two have a complex relationship constrained by the singularity. [ABSTRACT FROM AUTHOR]

We call a foliation (M, F) on a manifold M chaotic if it is topologically transitive and the union of closed leaves is dense in M. The foliated manifold M is not assumed to be compact. The chaotic foliations can be considered as multidimensional generalization of chaotic dynamical systems in the sense of Devaney. For foliations covered by fibrations we prove that a foliation is chaotic if and only if its global holonomy group is chaotic. We introduce the concept of the integrable Ehresmann connection for a foliation as a natural generalization of the integrable Ehresmann connection for smooth foliations. A description of the global structure of foliations with the integrable Ehresmann connection and a criterion for the chaotic behavior of such foliations are obtained. Applying the method of suspension, a new countable family of pairwise nonisomorphic chaotic foliations of codimension two on 3-dimensional closed and nonclosed manifolds is constructed. [ABSTRACT FROM AUTHOR]

This paper investigates the event-triggered impulsive synchronization of a variable-order fractional chaotic Lur'e system with the application of fractal interpolation based image encryption. The variable-order fractional Lur'e system is modeled into fractional order Chua's circuit model with short memory. The synchronization is achieved using event-triggered impulsive control and short memory for chaotic Lur'e systems, employing linear matrix inequalities. The variable-order fractional Chua's circuit systems successfully accomplish their synchronization using both impulsive and event-triggered impulsive control. Furthermore, fractal interpolation function (with function scalings) is applied to reconstruct the chaotic attractors. The Riemann-Liouville variable-order fractional calculus of diverse fractal functions is also investigated in connection with the study on variable-order fractional systems. The interpolated sequence, along with the Arnold transform, modified Fisher Yates algorithm, and additive diffusion, is utilized to propose an image encryption algorithm. Various statistical analyses are conducted to assess the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamic behaviors and chaos synchronization of the Chen system described by Caputo–Hadamard fractional derivative. First, the existence and uniqueness of a solution to the Chen system with Caputo–Hadamard derivative are proved by qualitative analysis. Further, the stability of equilibria of the considered system is analyzed with the aid of Routh–Hurwitz criteria. Meanwhile, the bifurcation condition of the Caputo–Hadamard Chen system is compared with the integer-order Chen system, where the differences between the two systems are demonstrated numerically. In the study of chaos synchronization of the drive–response Chen systems with Caputo–Hadamard derivative, two control schemes are developed: three nonlinear controllers and single linear controller. The feasibility of two control schemes is verified, and the synchronization performances of these two schemes are compared by numerical simulations. Based on this, the influence of the fractional-order on chaos synchronization performance is illustrated as well. [ABSTRACT FROM AUTHOR]

Motivated by the open problems on the global dynamics of the generalized four-dimensional Lorenz-like system, this paper deals with the existence of globally exponentially attracting sets and heteroclinic orbits by constructing a series of Lyapunov functions. Specifically, not only is a family of mathematical expressions of globally exponentially attracting sets derived, but the existence of a pair of orbits heteroclinic to  S 0  and  S ±  is also proven with the aid of a Lyapunov function and the definitions of both the  α -limit set and  ω -limit set. Moreover, numerical examples are used to justify the theoretical analysis. Since the obtained results improve and complement the existing ones, they may provide support in chaos control, chaos synchronization, the Hausdorff and Lyapunov dimensions of strange attractors, etc. [ABSTRACT FROM AUTHOR]

In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian Decomposition Method (ADM). Concurrently, the investigation probes into the existence of coexisting symmetric attractors, multiple coexisting bifurcation diagrams, and Lyapunov exponent spectra (LEs) utilizing system parameters as variables. Additionally, the system demonstrates an intriguing phenomenon known as offset boosting, where the embedding of an offset can adjust the position and size of the system's attractors. To ensure the practical applicability of these findings, a fractional-order sliding mode synchronization control scheme, inspired by integer-order sliding mode theory, is designed. The rationality and feasibility of this scheme are validated through a theoretical analysis and numerical simulation. [ABSTRACT FROM AUTHOR]

In multilayer complex networks, the uncertainty in node states leads to intricate behaviors. It is, therefore, of great importance to be able to estimate the states of target nodes in these systems, both for theoretical advancements and practical applications. This paper introduces a state observer-based approach for the state estimation of such networks, focusing specifically on a class of complex dynamic networks with nodes that correspond one-to-one. Initially, a chaotic system is employed to model the dynamics of each node and highlight the essential state components for analysis and derivation. A network state observer is then constructed using a unique diagonal matrix, which underpins the driver and response-layer networks. By integrating control theory and stability function analysis, the effectiveness of the observer in achieving synchronization between complex dynamic networks and target systems is confirmed. Additionally, the efficacy and precision of the proposed method are validated through simulation. [ABSTRACT FROM AUTHOR]

This article focuses on the synchronization problem of delayed chaotic neural networks via adaptive impulsive control. An adaptive impulsive gain law in a discrete-time framework is designed. The delay is handled skillfully by using the Lyapunov–Razumikhin method. To improve the flexibility of impulsive control, an event-triggered impulsive strategy to determine when the impulsive instant happens is designed. Additionally, it is proved that the event-triggered impulsive sequence cannot result in the occurrence of Zeno behavior. Some criteria are derived to guarantee synchronization for delayed chaotic neural networks. Eventually, an illustrative example is presented to empirically validate the effectiveness of the suggested strategy. [ABSTRACT FROM AUTHOR]

A current challenge with adaptive controllers is to define efficient tuning methods of the controller parameters. Unlike linear systems, nonlinear systems may need parameters that are continuously tuned at different operating points to provide stability and desired behaviours. This study aims to develop a solution for tuning proportional–integral–derivative (PID) controller parameters as opposed to changing the operating points of a nonlinear system. Most tuning methods calculate parameters according to the system's step or frequency response. However, adaptive controllers have self-tuneable parameters or control rules. The proposed algorithm in this paper contains a controller, an estimator, and a reference model, and uses the system model. Unlike the model reference adaptive control method, the proposed controller has tuneable controller parameters estimated by the extended Kalman–Bucy filter. The filter estimates the controller parameters to make the system perform like the auxiliary ideal reference model to ensure minimum-time consumption. Hence, this study aims to develop an algorithm that will automatically calculate controller parameters for each operating point of the controlled chaotic or nonlinear system to minimize settling time at each operating point. The proposed algorithm is implemented in a unified chaotic system in which the estimator and controller of the system run together. Simulation results confirm the performance of the proposed algorithm. In addition, the simulation results provide strong evidence that the proposed algorithm can be an effective tool for controlling nonlinear or chaotic systems. [ABSTRACT FROM AUTHOR]

Summary: The concerns of this article is to investigate the fixed time function combination synchronization (FCS) among three different chaotic systems with disturbances. First, a new stability theorem is presented by virtue of the integral inequality technique and a more accurate upper estimation of the convergence time is given. Next, the fixed time FCS problem is considered for the perturbed chaotic systems in which the scaling functions are generated by the bounded dynamical systems. Besides, the synchronization time is related to the control parameters rather than the initial values. The time upper bound can be calculated out by the simple formula, which is the function of control parameters. Finally, a simulation example is provided to illustrate the correctness of the derived criteria. [ABSTRACT FROM AUTHOR]

A new scheme is proposed for the synchronization transmission of the chaotic signals within a quantum network composed of the Dicke models with uncertain parameters. Considering that the chattering occurrence in the existing sliding mode control technique due to the general sliding mode surface is only dependent on the error variables, we put forward the novel design strategy of the sliding mode surface which is not only related to the error variables, but also the element of differential–integral is added into the sliding mode surface, which enables the synchronization transmission technique can flexibly adjust the speed of synchronous transmission and eliminate the chattering phenomenon during the synchronous transmission of quantum chaotic signal. The simulation results illustrate that the quantum signal from a single Dicke chaotic system can be transmitted synchronously among all nodes within the designed network with arbitrary topology and node number, and simultaneously the uncertain parameters belonging to the Dicke chaotic systems are also accurately identified, indicating that the design of the signal synchronization transmission controller and the identification law of the uncertain parameters based on the modified sliding mode technique proposed in this work are reasonable and feasible. [ABSTRACT FROM AUTHOR]

The asymptotic synchronization problem of chaotic Lur'e systems in the master-slave framework was explored in this paper. A time-varying delay feedback controller with quantization considerations and a delay-product-type Lyapunov-Krasovskii functional technique were employed to tackle this problem. Consider an error system based on master and slave systems, for which sufficient asymptotic stability requirements are developed to assure that the addressed system achieves proper synchronization. Following that, the desired control gain was determined by finding a feasible solution to these stability requirements. The results of this paper were validated using a numerical example with simulations, which revealed that they were superior to previously published ones. [ABSTRACT FROM AUTHOR]

Based on the fractional calculus and sliding mode control (SMC) techniques, this paper presents a predefined-time synchronization scheme for fractionalorder chaotic systems (FOCSs). Firstly, a predefined-time control method is proposed for fractional-order systems. Subsequently, a novel sliding surface is presented to ensure predefined-time convergence of the synchronization error. Then, a controller is designed by combining the predefined-time stability and the SMC method to ensure that the synchronization error converges to zero within the predefined time. Finally, the feasibility and robustness of the scheme are illustrated with two numerical simulation examples. [ABSTRACT FROM AUTHOR]

The purpose of this research is to investigate the synchronization and control for uncertain memristor-based cellular neural network and its application in secure communication. To address the issue, a novel sliding mode function is designed, on which the system states can effectively converge to the equilibrium point after reaching the sliding mode surface. Moreover, the corresponding controller is constructed by employing the proposed sliding mode function. The proposed control strategy achieves the synchronization of the uncertain memristor-based cellular neural network, and effectively addresses the integral saturation existing in traditional one. In addition, the control performance, including convergence speed, control accuracy, robustness and security, are significantly enhanced. Furthermore, the stability of the system is discussed based on Lyapunov theory. Finally, comparative tests and application examples are presented to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In general, the construction of observers for nonlinear descriptor systems depends on the solvability of a linear matrix inequality involving system matrices, and it is based on the system's nonlinearity. Therefore, the type of nonlinearity present in the system heavily affects the observer design process. There are significant developments in the literature for observer design for descriptor systems with various types of nonlinearity. Motivated by this, the current work reviews the literature on observer design for nonlinear descriptor systems with an extensive discussion on the type of nonlinearities that are considered. Here, an analysis and the comparison on the most common nonlinearities is presented, providing a roadmap to all researchers in the field. Furthermore, less common nonlinearities have been identified, presenting under-explored areas within the literature, and can open new domains for future research. [ABSTRACT FROM AUTHOR]

This paper proposes a novel five-dimensional (5D) memristor-based chaotic system by introducing a flux-controlled memristor into a 3D chaotic system with two stable equilibrium points, and increases the dimensionality utilizing the state feedback control method. The newly proposed memristor-based chaotic system has line equilibrium points, so the corresponding attractor belongs to a hidden attractor. By using typical nonlinear analysis tools, the complicated dynamical behaviors of the new system are explored, which reveals many interesting phenomena, including extreme homogeneous and heterogeneous multistabilities, hidden transient state and state transition behavior, and offset-boosting control. Meanwhile, the unstable periodic orbits embedded in the hidden chaotic attractor were calculated by the variational method, and the corresponding pruning rules were summarized. Furthermore, the analog and DSP circuit implementation illustrates the flexibility of the proposed memristic system. Finally, the active synchronization of the memristor-based chaotic system was investigated, demonstrating the important engineering application values of the new system. [ABSTRACT FROM AUTHOR]

This study investigates the dynamics of a modified Colpitts oscillator, exhibiting complex periodic and chaotic behaviors. Our research explores the dynamics and synchronization of coupled chaotic Colpitts oscillators, crucial for understanding their potential applications and behaviors. The main discovery is the emergence of a phase in which the systems achieve either complete synchronization or desynchronization. This behavior depends on the values of the coupling parameter. The subsequent challenge involves understanding how the coupling parameter influences the emergence of this synchronization phenomenon. [ABSTRACT FROM AUTHOR]

While increasingly complex algorithms are being developed for graph classification in highly-structured domains, such as image processing and climate forecasting, they often lead to over-fitting and inefficiency when applied to human interaction networks where the confluence of cooperation, conflict, and evolutionary pressures produces chaotic environments. We propose a graph transformation approach for efficient classification in chaotic human systems that is based on game theoretic, network theoretic, and chaos theoretic principles. Graph structural properties are compiled into time-series that are then transposed into the frequency domain to offer a dynamic view of the system for classification. We propose a set of benchmark data sets and show through experiments that the approach is efficient and appropriate for many dynamic networks in which agents both compete and cooperate, such as social media networks, stock markets, political campaigns, legislation, and geopolitical events. [ABSTRACT FROM AUTHOR]

A secure encryption scheme, combining multi-objective particle swarm optimization (MOPSO), optical chaos, and DNA algorithm is proposed and demonstrated. In this paper, a secure encryption and decryption architecture based on optical chaotic synchronization system with injection-locking is analyzed. We prove that a main laser (ML) can drive two-pair secondary lasers (TPSLs) to generate the synchronized optical chaos with high complexity. The system employs the XOR operation between the Hash value of the initial image and optimized value by MOPSO, which modulates the bias current of ML, thus TPSLs are driven to generate two pair synchronized chaotic sequences, which combine the Hash value of the initial image to generate two keys through a certain algorithm. Furthermore, two keys are used to scramble the pixel positions of the image and diffuse image pixels through DNA rules, and then in receiving end, two same keys are used to unscramble and reversely diffuse the encrypted image. Besides modulating the bias current of ML, the other aim of MOPSO is to optimize the entropy of the encrypted image and the correlation between the adjacent pixels. In order to ensure the recovery of real image, we compute and compare the digest-message of two pair synchronized chaotic sequences by using Hash algorithm in two ends before transmitting the encrypted image over optical fiber link. By synchronizing with the lasers at the sending end, we obtained two same keys to decrypt the ciphertext image in the receiving end. The simulation results show that this scheme can achieve secure communication of image against various attacks by analyzing and testing the security of the encrypted image. [ABSTRACT FROM AUTHOR]

We proposed and verified a scheme of chaos synchronization for integrated five-section semiconductor lasers with matching parameters. The simulation results demonstrated that the integrated five-section semiconductor laser could generate a chaotic signal within a large parameter range of the driving currents of five sections. Subsequently, chaos synchronization between two integrated five-section semiconductor lasers with matched parameters was realized by using a common noise signal as a driver. Moreover, it was found that the synchronization was sensitive to the current mismatch in all five sections, indicating that the driving currents of the five sections could be used as keys of chaotic optical communication. Therefore, this synchronization scheme provides a candidate to increase the dimension of key space and enhances the security of the system. [ABSTRACT FROM AUTHOR]

Due to the very complex algebraic structure of hyperchaotic models, it is often difficult to determine their limits. Using Lyapunov’s stability theory and optimization methods, we study the limits of a new 4D hyperchaotic Lorenz model. Based on the results obtained, we study complete chaotic synchronization. Finally, to demonstrate the effectiveness of the proposed chaotic synchronization scheme, some numerical simulations are provided. [ABSTRACT FROM AUTHOR]

Developing chaotic systems-on-a-chip is gaining much attention due to its great potential in securing communication, encrypting data, generating random numbers, and more. The digital implementation of chaotic systems strives to achieve high performance in terms of time, speed, complexity, and precision. In this paper, the focus is on developing high-speed Field Programmable Gate Array (FPGA) cores for chaotic systems, exemplified by the Lorenz system. The developed cores correspond to numerical integration techniques that can extend to the equations of the sixth order and at high precision. The investigation comprises a thorough analysis and evaluation of the developed cores according to the algorithm complexity and the achieved precision, hardware area, throughput, power consumption, and maximum operational frequency. Validations are done through simulations and careful comparisons with outstanding closely related work from the recent literature. The results affirm the successful creation of highly efficient sixth-order Lorenz discretizations, achieving a high throughput of 3.39 Gbps with a precision of 16 bits. Additionally, an outstanding throughput of 21.17 Gbps was achieved for the first-order implementation coupled with a high precision of 64 bits. These outcomes set our work as a benchmark for high-performance characteristics, surpassing similar investigations reported in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose an analytical approach to estimate the largest Lyapunov exponent (LLE) of a Rössler chaotic system, leveraging the synchronization method. This research focuses on establishing an analytical criterion for the synchronization of two identical Rössler chaotic systems through the linear coupling of state variables. This is crucial because the LLE of such systems can be estimated based on the critical coupling required for synchronization. Unlike previous studies, we first transform the synchronization error system between two identical Rössler chaotic systems into a set of Volterra integral equations by using the Laplace transform and convolution theorem. The critical coupling for synchronization is analytically derived using integral equation theory to solve the error system. As compared to the numerical results of the Rössler chaotic system's LLE, our analytical estimates demonstrate high accuracy. Our findings suggest that the challenge of estimating the Rössler chaotic system's LLE can be simplified to solving a cubic algebraic equation, offering a novel perspective on the analysis of how parameters influence the LLE's value in the Rössler chaotic system. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive terminal sliding-mode control (ATSMC) method is proposed for the synchronization of uncertain fractional-order chaotic systems with disturbances. According to the sliding-mode control theory, a non-singular sliding surface is constructed. To overcome the chattering problem of ATSMC, a smooth term is used in the controller. In order to reduce the estimation error of an uncertain parameter, adaptive laws are designed to adjust the amplitude of the continuous function. Based on the Lyapunov stability theory, a stability analysis of the error system is performed to ensure that the tracking error eventually converges to the origin. The effectiveness and applicability of the proposed control strategy are verified using the simulation results. [ABSTRACT FROM AUTHOR]

This paper analyzes the complete synchronization of a three-layer Rulkov neuron network model connected by electrical synapses in the same layers and chemical synapses between adjacent layers. The outer coupling matrix of the network is not Laplacian as in linear coupling networks. We develop the master stability function method, in which the invariant manifold of the master stability equations (MSEs) does not correspond to the zero eigenvalues of the connection matrix. After giving the existence conditions of the synchronization manifold about the nonlinear chemical coupling, we investigate the dynamics of the synchronization manifold, which will be identical to that of a synchronous network by fixing the same parameters and initial values. The waveforms show that the transient chaotic windows and the transient approximate periodic windows with increased or decreased periods occur alternatively before asymptotic behaviors. Furthermore, the Lyapunov exponents of the MSEs indicate that the network with a periodic synchronization manifold can achieve complete synchronization, while the network with a chaotic synchronization manifold can not. Finally, we simulate the effects of small perturbations on the asymptotic regimes and the evolution routes for the synchronous periodic and the non-synchronous chaotic network. [ABSTRACT FROM AUTHOR]

This paper studies the synchronization and control of chaotic systems while proposing a novel chaotic-based path-tracking application for mobile robots (MRs) to ensure their safety and security. In security-based applications that use MRs, such as patrol MRs, the path of the MRs must be complex enough to prevent easy prediction. Multiple chaotic systems with a chaotic switching mechanism are introduced for secure path planning. The main challenges are that the dynamics of MRs are entirely unknown. The modeled dynamics of the MRs are unreliable in practice due to a broad range of uncertainties related to the parameters, operating conditions, environmental impacts, time delays, unmodeled frictions, noisy sensors, and faulty actuators. Also, the chaotic switching of reference signals between chaotic signals imposes a high dynamic perturbation. The main novelties are as follows: (1) a strong secure path is introduced for MRs. (2) A powerful fractional-order predictive controller using type-3 (T3) fuzzy-logic systems (FLSs) is developed. (3) The estimation and prediction errors of T3-FLSs are compensated by a designed parallel compensator. (4) T3-FLSs are tuned online, such that stability is ensured, and prediction accuracy is guaranteed. (5) The suggested scheme is implemented on a real-world MR, and the results demonstrate the feasibility and accuracy of the proposed method. Also, in several simulations, the efficacy of the introduced controller is examined. [ABSTRACT FROM AUTHOR]

In this paper, a new scheme of anti difference multiswitching compound compound combination synchronization for achieving synchronization between seven chaotic systems has been proposed. This novel scheme of synchronization involves five drive systems and two response systems and its first of a kind. Due to multiswitching of signals, the security of signals transmitted through the systems enhances. Nonlinear controllers have been designed and synchronization has been achieved between the drive and response systems using Lyapunov stability criteria. Theoretical results have been given and numerical simulations have been performed using MATLAB to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The exploration of chaos, synchronization, and circuit implementation in analog simulations unveils a versatile framework with diverse applications. Originating from a universal chaos model rooted in laser physics, its adaptability extends to neural dynamics and random number generation, where both rely on characteristic time scales. Circuit implementations using op-amps and analog multipliers offer tangible avenues for exploration. However, challenges like bias and trajectory distortion drive the need for innovative solutions. Through numerical integration and circuit simulations, analysis of chaotic regimes such as Sub-harmonic Chaos (SC) and Homoclinic Chaos (HC) reveals crucial behaviors for applications like secure communications. Despite experimental hurdles, advancements in circuit design promise novel pathways for chaos synchronization studies. Understanding the intricate interplay between chaos and these systems is vital, given their reliance on characteristic time scales. Additionally, exploring chaos synchronization, especially within analog circuits, shows potential for revolutionizing information processing capabilities, despite inherent challenges. Progress in circuit design persists, forging new avenues in chaos synchronization studies, shaping a dynamic landscape poised for further exploration and innovation.

ABSTRACTThe inherent randomness in economic factors causes complex and irregular behaviour that affects financial system stability and economic growth. Such chaotic behaviour can make it difficult to synchronize financial systems. The chaotic finance system synchronization precision maintains financial stability and economic growth. In this paper, the controller design procedure assumes that the financial system is exposed to unknown bounded exogenous disturbances and model uncertainties. This research proposes a novel direct adaptive control strategy that achieves robust synchronization of two identical four-dimensional finance chaotic (FDFC) systems. The proposed controller establishes a faster, smoother synchronization error vector convergence to zero. The controller design procedure does not eliminate the closed-loop's nonlinear terms and is independent of the financial system parameters. These controller's attributes accomplish the closed-loop robust performance. Further, this controller uses real-time estimates of unknown model uncertainties and bounds to compensate for unknown exogenous disturbances. Computer simulation results and proofs of theoretical analysis based on the Lyapunov stability theory confirm that the proposed control technique compels the error vector trajectories to the origin in a short transient time with less active oscillations for all signals. The paper includes comparative computer simulations for verifying the theoretical findings.

This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua's circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm's robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security. [ABSTRACT FROM AUTHOR]

This paper proposes an online monitoring and defect identification method for XLPE power cables using harmonic visualization of grounding currents. Four typical defects, including thermal aging, water ingress and dampness, insulation scratch, and excessive bending, were experimentally conducted. The AC grounding currents of the cable specimens with different defects were measured during operation. By using the chaotic synchronization system, the harmonic distortion was transformed into a 2D scatter diagram with distinctive characteristics. The relationship between the defect type and the diagram features was obtained. A YOLOv5 (you only look once v5) target recognition model was then established based on the dynamic harmonics scatter diagrams for cable defect classification and identification. The results indicated that the overall shape, distribution range, density degree, and typical lines formed by scatter aggregation can reflect the defect type effectively. The proposed method greatly reduces the difficulty of data analysis and enables rapid defect identification of XLPE power cables, which is useful for improving the reliability of the power system. [ABSTRACT FROM AUTHOR]

We experimentally investigate the forced synchronization of a self-excited chaotic thermoacoustic oscillator with two natural frequencies, f1 and f2. On increasing the forcing amplitude, xf, at a fixed forcing frequency, ff, we find two different types of synchronization: (i) ff/f1 = 1: 1 or 2: 1 chaos-destroying synchronization (CDS), and (ii) phase synchronization of chaos (PSC). En route to 1: 1 CDS, the system transitions from an unforced chaotic state (CH1,2) to a forced chaotic state (CH1,2,f), then to a two-frequency quasiperiodic state where chaos is destroyed (T²2,f), and finally to a phase-locked period-1 state (P1f). The route to 2: 1 CDS is similar, but the quasiperiodic state hosts a doubled torus (2T²2,f) that transforms into a phase-locked period-2 orbit (P2f) when CDS occurs. En route to PSC, the system transitions to a forced chaotic state (CH1,2,f) followed by a phase-locked chaotic state, where f1, f2 and ff still coexist but their phase difference remains bounded. We find that the maximum reduction in thermoacoustic amplitude occurs near the onset of CDS, and that the critical xf required for the onset of CDS does not vary significantly with ff. We then use two unidirectionally coupled Anishchenko-Astakhov oscillators to phenomenologically model the experimental synchronization dynamics, including (i) the route to 1: 1 CDS, (ii) various phase dynamics, such as phase drifting, slipping and locking, and (iii) the thermoacoustic amplitude variations in the ff/f1-xf plane. This study extends the applicability of open-loop control further to a chaotic thermoacoustic system, demonstrating (i) the feasibility of using an existing actuation strategy to weaken aperiodic thermoacoustic oscillations, and (ii) the possibility of developing new active suppression strategies based on both established and emerging methods of chaos control. [ABSTRACT FROM AUTHOR]

We numerically investigate the forced synchronization of the self-excited flow behind a plunging airfoil in ground effect at a Reynolds number of Re = 1000. On varying the plunging amplitude and frequency, we find a rich array of nonlinear dynamics, such as a period-1 limit cycle due to natural vortex shedding as well as two-frequency quasiperiodicity on a torus attractor ( T 2 ). For certain non-resonant plunging frequencies without a ground surface, we find that low-dimensional chaos emerges via the Ruelle–Takens–Newhouse route. However, we find that the chaos can be suppressed by introducing a ground surface, inducing a direct transition from T 2 quasiperiodicity to 1:1 phase locking as the plunging amplitude rises over the boundaries of the Arnold tongue. Apart from suppressing chaos, the ground surface also causes the lift and drag coefficients to become less sensitive to the plunging motion itself. Knowledge of the critical plunging conditions required for forced synchronization and chaos could be useful in various engineering applications, such as the design of pico air vehicles. [ABSTRACT FROM AUTHOR]

This research paper focuses on investigating the dynamics and chaos control of two discrete systems corresponding to the singularly perturbed equation associated to the Hénon difference equation with continuous arguments. We investigate the local stability of the two systems. To achieve chaos control, we employ the state feedback control method for both systems. Numerical simulations are conducted to gain insights into the qualitative behavior of these systems. By conducting numerical simulations, we gain valuable insights into the role played by the perturbation parameter and the discrete delays in the bifurcation behavior of each system. Furthermore, we demonstrate the practical application of the chaos control method through the implementation of an on-off strategy. [ABSTRACT FROM AUTHOR]