Synchronization Of Time-delayed Chaotic Systems Research Articles

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

This paper deals with the fixed-time adaptive time-varying matrix projective synchronization (ATVMPS) of different dimensional chaotic systems (DDCSs) with time delays and unknown parameters. Firstly, to estimate the unknown parameters, adaptive parameter updated laws are designed. Secondly, to realize the fixed-time ATVMPS of the time-delayed DDCSs, an adaptive delay-unrelated controller is designed, where time delays of chaotic systems are known or unknown. Thirdly, some simple fixed-time ATVMPS criteria are deduced, and the rigorous proof is provided by employing the inequality technique and Lyapunov theory. Furthermore, the settling time of fixed-time synchronization (Fix-TS) is obtained, which depends only on controller parameters and system parameters and is independent of the system’s initial states. Finally, simulation examples are presented to validate the theoretical analysis.

Adaptive Modulus Hybrid Projective Combination Synchronization of Time-Delay Chaotic Systems with Uncertainty and Disturbance and its Application in Secure Communication

Adaptive Modulus Hybrid Projective Combination Synchronization of Time-Delay Chaotic Systems with Uncertainty and Disturbance and its Application in Secure Communication

Adaptive Synchronization of Time-Delay Chaotic Systems with Intermittent Control

Abstract Time delay is a common but not negligible phenomenon in nonlinear systems, which affects the performance of synchronization. Based on principles of intermittent control and Lyapunov stability theories, we establish the synchronization criteria of the time-delay chaotic systems via adaptive intermittent control. The proposed control scheme is under aperiodically intermittent control, which is also extended to periodically intermittent control to better realization. Finally, to verify the effectiveness of our results, we choose the Lorenz system to do simulation.

Synchronization of Time-delay Chaotic Systems with Uncertainties and External Disturbances

In this article, the authors have studied the problem of synchronization of time-delay chaotic systems with uncertainties and external disturbances. The effectiveness of the problem statement is visualized through synchronization of time-delay advanced Lorenz system and double time-delay R¨ossler system with parametric uncertainties and disturbances using active control method. Numerical simulations are carried out using Runge-Kutta algorithm for delay differential equations (DDEs) and the results are depicted through graphs. The physical meaning of time-delay system is that a signal is transmitted and received at a later time, which is found to occur in active sensing problems. The salient feature of the article is the demonstration of the efficiency of the considered method during synchronization of time-delay chaotic systems even in presence of uncertainties and external disturbances.

A single finite-time synchronization scheme of time-delay chaotic system with external periodic disturbance

In this paper, dynamical behaviors of three-dimensional chaotic system with time-delay and external periodic disturbance are investigated. When the periodic perturbation term and time-delay are added, the system presents more abundant dynamic behaviors, which can be switched between periodic state and chaotic state. Based on Lyapunov stability theory, a sufficient condition for finite-time synchronization is given. A single controller is proposed to realize finite-time synchronization of time-delay chaotic system with external periodic disturbance. The addressed scheme is provided in the form of linear inequality which is simple and easy to be realized. At the same time, it also displays that when delay term \begin{document}$ \tau $\end{document} takes different values, the time of synchronization shows certain difference. The feasibility and effectiveness of the finite-time synchronization method is verified by theoretical analysis and numerical simulation.

Combination synchronization of time-delay chaotic system via robust adaptive sliding mode control

In this paper, the methodology to achieve combination synchronization of time-delay chaotic system via robust adaptive sliding mode control is introduced. The methodology is implemented by taking identical time-delay Lorenz chaotic system. The selection of switching surface and the design of control law is also discussed, which is an important issue. By utilizing rigorous mathematical theory, sufficient condition is drawn for the stability of error dynamics based on Lyapunov stability theory. Theoretical results are supported with the numerical simulations. The complexity of this methodology is useful to strengthen the security of communication. The hidden message can be partitioned into several parts loaded in two master systems to improve the accuracy of communication.

A medical image encryption algorithm based on synchronization of time-delay chaotic system

This paper presents a new synchronization method of the time-delay chaotic system and its application in medical image encryption. Compared with the existing techniques, the error system is greatly simplified because many coupled items can be considered zero items. An improved image encryption scheme based on a dynamic block is proposed. This scheme divides the image into dynamic blocks, and the number of blocks is determined by a previous block cipher. Numerical simulations are provided to illustrate the effectiveness of the proposed method.

Combined synchronization of time-delayed chaotic systems with uncertain parameters

The article presents combined synchronization among time delayed chaotic systems in the presence of uncertain parameters using nonlinear control method. Control functions are designed to achieve combined synchronization using Lyapunov-Krasovskii function for stability analysis. The synchronization among three and four time delayed chaotic systems have been shown as examples of combined synchronization. Double delay Rossler system, the advanced Lorenz system, time delay Liu and Chen systems have been taken to show the combined synchronization. Numerical simulation and graphical results are carried out using Runge–Kutta method for delay-differential equations, which show that the designing of control functions are very effective and reliable and can be applied for combined synchronization among time-delayed chaotic systems.

Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication

This paper presents finite-time chaos synchronization of time-delay chaotic systems with uncertain parameters. According to the proposed method, a lot of coupled items can be treated as zero items. Thus, the whole system can be simplified greatly. Based on robust chaotic synchronization, secure communication can be realized with a wide range of parameter disturbance and time-delay. Numerical simulations are provided to illustrate the effectiveness of the proposed method.

Reduced-order synchronization of time-delay chaotic systems with known and unknown parameters

In this article, a novel robust nonlinear controller approach is focused to study theoretically, the reduced-order synchronization phenomena of two unrelated time-delayed chaotic systems under the determined and unknown parameters. It is assumed that the two systems are perturbed by the bounded unstructured uncertainties and unknown external disturbance. Based on the Lyapunov–Krasovskii functional theory, a robust nonlinear synchronization controller is focused and a suitable Lyapunov functional is constructed so that they establish the globally asymptotical stability of the closed-loop at the origin. Subsequently, suitable adaptive laws of unknown parameters are designed to identify the unknown parameters. Finally, the effectiveness of the proposed reduced-order synchronization approach is verified by numerical simulations. A brief comparison of the present study with prior works has been given.

Lag-generalized synchronization of time-delay chaotic systems with stochastic perturbation

The lag-generalized synchronization of coupled time-delay chaotic systems with unknown parameters and stochastic perturbation is investigated. Based on the LaSalle-type invariance principle of stochastic differential equation, the synchronization is realized by analyzing stochastic stability of the error system. In order to achieve the synchronization, the unknown parameter update laws and the control laws are proposed. At last, two numerical examples are presented to show the effectiveness of the obtained theoretical results.

An answer to the open problem of $$\mathcal{L}_2 - \mathcal{L}_\infty$$ synchronization for time-delayed chaotic systems

In this paper, we deal with the open problem of \(\mathcal{L}_2 - \mathcal{L}_\infty\) synchronization for time-delayed chaotic systems with external disturbance. To date, a control scheme has been proposed to synchronize chaotic systems without time delay, but no solution exists for the case when chaotic systems have time delay. For the first time, in this paper, we prove that a new criterion for the \(\mathcal{L}_2 - \mathcal{L}_\infty\) synchronization of time-delayed chaotic systems exists.

Synchronization of Time-Delay Chaotic System in Presence of Noise

Abstract Chaotic synchronization, as a key technique of chaotic secure communication, has received much attention in recent years. This paper proposes a nonlinear synchronization scheme for the time-delay chaotic system in the presence of noise. In this scheme, an integrator is introduced to suppress the influence of channel noise in the synchronization process. The experimental results demonstrate the effectiveness and feasibility of the proposed scheme which is strongly robust against noises, especially the high-frequency noises.

Isochronal synchronization of time delay and delay-coupled chaotic systems

This paper studies the problem of isochronal synchronization of time-delay chaotic systems featuring also coupling delay. Based on the Lyapunov–Krasovskii stability theory, sufficient conditions are derived for the stability of isochronal synchronization between a pair of identical chaotic systems. Such criteria permit the proper design of stable proportional linear feedback controller, more specifically, the design of adequate proportional feedback gain matrices. The proposed criteria are suited to systems with (i) intrinsic delay, (ii) coupling delay or (iii) both. Numerical simulations of the synchronization of delay-coupled systems are presented as examples of the application of the criteria.

Dual-anticipating, dual and dual-lag synchronization in modulated time-delayed systems

In this Letter, dual synchronization in modulated time delay system using delay feedback controller is proposed. Based on Lyapunov stability theory, we suggest a general method to achieve the dual-anticipating, dual, dual-lag synchronization of time-delayed chaotic systems and we find both its existing and sufficient stability conditions. Numerically it is shown that the dual synchronization is also possible when driving system contain two completely different systems. Effect of parameter mismatch on dual synchronization is also discussed. As an example, numerical simulations for the Mackey–Glass and Ikeda systems are conducted, which is in good agreement with the theoretical analysis.

Projective synchronization with different scale factors in a driven–response complex network and its application in image encryption

We study projective (anticipatory, exact and lag) synchronization of time-delayed chaotic systems in a driven–response complex network (DRCN), where the nodes are not partially linear and the scale factors are different from each other. Two synchronization criteria are presented; the first is easy to satisfy with simple limitation and the second relaxes the previous limitation and can be executed only by adding a simple linear feedback control to every node. As a special case, projective synchronization in a DRCN without time delay is analyzed by using a different method. The corresponding synchronization criterion is given, which can be realized by adopting single-node adaptive control. This paper extends previous work, where the nodes of the DRCN are partially linear, there is limitation of the coupling matrix or the scale factors of the nodes are all equal. Numerical examples are given to demonstrate the effectiveness of the proposed synchronization criteria. Due to the complexity of the different scale factors, we select the chaotic data from the DRCN presented in this paper and apply the data selected in image encryption. Simulation results show that our method is efficient with a large key space, high sensitivity to initial conditions and high speed.

Synchronization of time-delay chaotic systems on small-world networks with delayed coupling

By using the well-known Ikeda model as the node dynamics, this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays. It shows that, in contrast with the undelayed case, networks with delays can actually synchronize more easily. Specifically, for randomly distributed delays, time-delayed mutual coupling suppresses the chaotic behaviour by stabilizing a fixed point that is unstable for the uncoupled dynamical system.

Formula omitted] synchronization of time-delayed chaotic systems

This paper considers H ∞ synchronization of a class of time-delayed chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the dynamic feedback controller is established to not only guarantee synchronization between derive and response systems, but also reduce the effect of external disturbance to an H ∞ norm constraint. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme.

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks, and we find both its existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey–Glass systems on Erdös–Rényi networks.

Parameter estimation for time-delay chaotic system by particle swarm optimization

The knowledge about time delays and parameters is very important for control and synchronization of time-delay chaotic system. In this paper, parameter estimation for time-delay chaotic system is given by treating the time delay as an additional parameter. The parameter estimation is converted to an optimization problem, which finds a best parameter combination such that an objective function is minimized. Particle swarm optimization (PSO) is used to optimize the objective function through particles’ cooperation and evolution. Two illustrative examples are given to show the validity of the proposed method.