Synchronization Of Chaotic Systems Research Articles

Synchronization of non-smooth chaotic systems via an improved reservoir computing

The reservoir computing (RC) is increasingly used to learn the synchronization behavior of chaotic systems as well as the dynamical behavior of complex systems, but it is scarcely applied in studying synchronization of non-smooth chaotic systems likely due to its complexity leading to the unimpressive effect. Here proposes a simulated annealing-based differential evolution (SADE) algorithm for the optimal parameter selection in the reservoir, and constructs an improved RC model for synchronization, which can work well not only for non-smooth chaotic systems but for smooth ones. Extensive simulations show that the trained RC model with optimal parameters has far longer prediction time than those with empirical and random parameters. More importantly, the well-trained RC system can be well synchronized to its original chaotic system as well as its replicate RC system via one shared signal, whereas the traditional RC system with empirical or random parameters fails for some chaotic systems, particularly for some non-smooth chaotic systems.

Two ZNN-Based Unified SMC Schemes for Finite/Fixed/Preassigned-Time Synchronization of Chaotic Systems

Two ZNN-Based Unified SMC Schemes for Finite/Fixed/Preassigned-Time Synchronization of Chaotic Systems

Numerical analysis of a chaotic coupled hyperbolic PDE system for secure image encryption

This paper focuses on the interest of using chaotic hyperbolic Partial Differential Equations (PDE) systems synchronization for secure image communication. Such systems offer a promising alternative to finite dimensional chaotic systems with enlarged key space, efficient computation, and more complex dynamics. Here, we modify the classical chaotic hyperbolic PDE system by adding integral boundary couplings and potential terms. The chaotic behaviour of the resulting system is observed in numerical simulations. Adding such couplings allows to enhance the security of the cryptosystem. The synchronization of receiver and transmitter chaotic systems is achieved by the use of a chaotic observer designed using the backstepping methodology. The initial image can then be encrypted into a chaotic signal on the transmitter side before being sent to the receiver side. Using observational data, the receiver can then reconstruct the initial image. Numerical illustrations complete the paper.

Discrete fractional order chaotic systems synchronization based on the variable structure control with a new discrete reaching-law

In this paper, we directly derive a new discrete state space expression of the fractional order chaotic system based on the fractional order Grnwald-Letnikow (G-L) definition and design a variable structure controller with a new faster reaching-law. The new reaching-law has the advantages of weakening the high frequency shake. Firstly, the condition of the discrete sliding mode surface is demonstrated. Then a multi-parametric function for sliding mode surface is constructed for weakening the high frequency shake through improving the Gao discrete reaching-law. Finally, the newly designed variable structure controller is applied to realize the synchronization of two different order discrete fractional chaotic systems. The simulation results show that the designed controller in this paper is effective, as it can achieve the synchronization of the discrete fractional order chaotic systems with external disturbances. Theoretical analysis and simulation results prove the effectiveness and robustness of this control method.

A Double Integral Noise-Tolerant Fuzzy ZNN Model for TVSME Applied to the Synchronization of Chua's Circuit Chaotic System

A Double Integral Noise-Tolerant Fuzzy ZNN Model for TVSME Applied to the Synchronization of Chua's Circuit Chaotic System

Finite and fixed-time synchronization of memristive chaotic systems based on sliding mode reaching law

Two innovative sliding mode control laws based on the convergence principle of reaching law are presented in this work. These control laws are used to achieve both finite-time and fixed-time synchronization for a specific class of memristive chaotic system, which are known for their intricate and complex dynamical behaviors. By utilizing these control strategies, we can effectively manage the synchronization process and ensure rapid convergence. Firstly, for the finite-time synchronization issue, a novel power reaching law is derived. Compared with the conventional reaching law, the reaching law presented in this work has a prominent advantage that the chattering of the sliding mode control is reduced to a lesser extent and the speed of reaching the sliding surface is quicker. An upper bound of the stabilization time, which is dependent on the initial conditions of the system, is obtained and the system is proved stable. For the fixed time synchronization problem, a new double power reaching law is put forward to minimize the chattering and accelerate the convergence. Then, by utilizing the fixed time stability theory, the upper bound of the convergence time that remains invariant with the initial value of the system is derived. Finally, in order to verify the effectiveness and feasibility of the theoretical derivation in this paper, two sets of control experiments are set up and the influences of the two control laws on the system synchronization state are compared. The experimental phenomenon strongly proves the accuracy of the proposed theorem.

Secure Communication via Chaotic Synchronization Based on Reservoir Computing.

Information security occupies a very important part of national security. Chaos communication can provide high-level physical layer security, but its harsh claims on the chaotic system parameters of the transmitter and the receiver resulting in reduced synchronization coefficient and more difficult consistent synchronization of point to multipoint networking. In this article, a chaotic synchronization and communication system based on reservoir computing (RC) has been proposed. In this scheme, the trained RC highly synchronized with the emitter acts as the receiver with simplified structure under the premise of ensuring safety. Simultaneously, the cross-prediction algorithm has been proposed to weaken the accumulation effect of prediction synchronization error of RC and facilitate the realization of long-term communication. Furthermore, the tolerance of the system performance to the signal-to-noise ratio with the variations of the mask coefficients has been investigated, and the optimal operation point under the condition of the adjustable number of nodes and leakage rate of RC has been numerically analyzed. The simulation results show that the normalized mean-square error of synchronization of 10⁻⁶ magnitude and the bit error rate of decryption at 10⁻⁸ level can be obtained. Finally, from the operational perspective, a 100-m short-distance experiment confirms that its communication performance is consistent with the simulation results. We strongly believe that the proposed system offers the opportunity of a new research direction in chaotic secure communications.

Robust synchronization of four-dimensional chaotic finance systems with unknown parametric uncertainties

ABSTRACT The 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.

A new 3D fractional-order chaotic system with complex dynamics

Compared to integer-order chaotic systems, fractional-order chaotic systems have more complex dynamical features due to the introduction of order. The application of fractional-order chaotic systems to chaotic cryptosystems makes the cryptosystems with higher security properties. In this paper, we developed a new 3D fractional-order chaotic system from a 3D integer-order chaotic system, and investigate the dynamical behaviors of this fractional-order system with different parameters and orders. Moreover, self-excited attractors appeared at lower orders through circuit simulations. Furthermore, the synchronization of the new fractional-order chaotic system in the presence of systematic uncertainties and perturbations was achieved using the sliding mode control technique, which sets the stage for the implementation of communication. Finally, offset boosting control was used to investigate the utility of the new chaotic system in engineering applications.

The adaptive sliding synchronization of uncertain Duffing-Holmes fractional-order chaotic systems with dead-zone

This article investigates the problem of adaptive sliding synchronization for Duffing-Holmes fractional-order chaotic systems in the presence of dead-zone, disturbance, and uncertainty. It starts by estimating dead-zone parameters, and then adaptive laws are used to compensate the dead-zone parameters. In the second step, a sliding mode controller is designed so that the slave system can follow the master system. The fractional type of Lyapunov is implemented to prove stability. The proposed adaptive sliding mode controller guarantees the asymptotic stability of system despite the presence of the dead-zone and uncertainty. Simulation results show the validity and effectiveness of the proposed controller for synchronization of Duffing-Holmes fractional-order chaotic systems perturbed by the dead-zone, disturbance, and uncertainty.

Opposition to Synchronization of Bistable State in Motif Configuration of Rössler Chaotic Oscillator Systems

This paper presents the study of the opposition to the synchronization of bistable chaotic oscillator systems in basic motif configurations. The following configurations were analyzed: Driver-response oscillator systems coupling, two driver oscillator systems to one response oscillator, and a three-oscillator systems ring unidirectional configuration. The study was conducted using the differential equations representing the piecewise linear Rössler-like electronic circuits; the initial conditions were changed to achieve a bistable characteristic Homoclinic H-type or Rössler R-type attractor. Analyzing a sweep of the initial conditions, the basin attractor was obtained. It can be observed that each system has a preferred Homoclinic chaotic attractor with any perturbation or change in initial conditions. A similarity analysis based on the coupling factor was also performed and found that the system has a preferentially Homoclinic chaotic attractor.

Dynamic Analysis and Adaptive Synchronization of a New Chaotic System

Dynamic Analysis and Adaptive Synchronization of a New Chaotic System

Matrix and Inverse Matrix Projective Synchronization of Chaotic and Hyperchaotic Systems with Uncertainties and External Disturbances

Matrix and Inverse Matrix Projective Synchronization of Chaotic and Hyperchaotic Systems with Uncertainties and External Disturbances

Back-stepping projective synchronization of fractional-order unified systems based on the lower triangular structure

The synchronization of fractional-order chaotic systems (FOCSs) plays an important role in modern control theory, the projective synchronization (PS) as a class of synchronization problems, also has huge applications and has attracted much attention. It is, however, shown in the obtained literature that the results on the PS of FOCSs either loss the rigorous theoretical demonstration or verify from the viewpoint of numerical simulations. How to derive a necessary and sufficient condition to guarantee the PS of complex FOCSs by a simple controller is still open. To this end, this article is concerned with the PS of fractional-order unified systems (FO-USs) that are important in FOCSs covering fractional-order Lorenz, Chen and Lü systems, where the controller is presented based on the lower triangular structure by use of the back-stepping technique. The necessary and sufficient criterion for the PS of FO-USs is proposed by solving an algebraic equation, and the controller for the PS of FO-USs is derived based on the lower triangular structure combined with back-stepping approach. Finally, the simulation results are reported to verify the correctness and efficiency of the obtained results.

Adaptive finite-time synchronisation of variable-order fractional chaotic systems for secure communication

The variable-order fractional (VOF) chaotic systems offer a promising solution for applications in secure communication due to their unique properties. This paper addresses the synchronisation problem in secure communication for these systems, which have uncertainties and external disturbances with unknown bounds. According to the variable-order fractional type Mittag-Leffler stability theorem, a fractional-order derivative is applied to a sliding surface, and suitable adaptive laws are devised to address uncertainties and disturbances. A variable-order fractional control strategy and a new criterion are developed to ensure the synchronisation error systems achieve asymptotic stability in finite time, for which the upper limit can be obtained. Simulation outcomes demonstrate the efficacy of the proposed synchronisation strategy in secure communication scenarios.

Control & synchronization of a unified chaotic system using an adaptive controller with an extended Kalman–Bucy-filter based Auto-Tuner

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.

A chaotic synchronization system based on memristor for weak signal detection and its circuit implementation

A chaotic synchronization system based on memristor for weak signal detection and its circuit implementation

A strong secure path planning/following system based on type-3 fuzzy control, multi-switching chaotic systems, and random switching topology

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.

Finite-time synchronization of fractional multi-wing chaotic system

The objective of this article is to obtain multi-wing chaotic attractors of fractional chaotic systems through computerized symbolic computation. By applying the Julia fractal technique, the different number wing attractors are constructed for proposed equations. Moreover, the dynamics of the multi-wing system are analyzed by phase diagram, Poincare mapping, etc Consequently, the system exhibits complex dynamics, and the motion states at different order can be known from the bifurcation diagram with the change of order. Additionally, aiming at multi- wing fractional chaotic system, the controllers are designed, and the finite time synchronization control of the proposed system is performed. The results prove that the proposed finite-time synchronization method has important research value in the field of engineering.

Dynamical analysis and finite-time synchronization of grid-scroll memristive chaotic system without equilibrium

The study of multi-scroll memristive chaotic system has attracted great interest due to their unique dynamics. In this paper, a novel five-dimensional chaotic system devoid of equilibria is constructed by introducing two memristors into a three-dimensional chaotic system, resulting in the emergence of a grid-scroll attractor. The evolution of the chaotic system is analyzed using techniques such as phase diagrams, Poincare maps, bifurcation diagrams, and Lyapunov exponents. The basin of attraction is delineated to investigate the coexisting attractors in the system. By manipulating the parameters, the partial amplitude of the system can be modulated. To experimentally confirm the existence of the proposed system, a circuit is meticulously designed and implemented. At last, an adaptive controller is designed, and it is observed from the simulation results that a synchronization state can be reached by the two chaotic systems within a finite time.