Criteria For Global Synchronization Research Articles

Global Synchronization of Discrete-Time Dynamical Network With a Directed Graph

We investigate synchronization of linearly coupled map lattices with asymmetric and irreducible coupling matrices. In terms of graph terminology, the coupling matrix represents a directed graph. In case the uncoupled map satisfies Lipschitz conditions, a criterion of global synchronization of the linearly coupled map lattices is derived. With this criterion, we investigate how synchronizability depends on the coupling matrix as well as graph topology. Furthermore, we also prove that a directed graph can synchronize some chaotic map if and only if the graph contains a spanning tree

Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control

The paper deals with a linear state error feedback control technique which is utilized to synchronize two parametrically excited non-autonomous Duffing oscillators. Some sufficient criteria for global chaos synchronization are obtained by means of Lyapunov’s direct method. A few examples are illustrated to verify the proposed theoretical results.

Chaos Synchronization Criterion and Its Optimizations for aNonlinear Transducer System via Linear State Error Feedback Control

Global chaos synchronization of two identical nonlinear transducersystems is investigated via linear state error feedback control. Thesufficient criterion for global chaos synchronization is derived firstlyby the Gerschgorin disc theorem and the stability theory of lineartime-varied systems. Then this sufficient criterion is further optimizedin the sense of reducing the lower bounds of the coupling coefficientswith two methods, one based on Gerschgorin disc theorem itself and theother based on Lyapunov direct method. Finally, two optimized criteriaare compared theoretically.

The synchronization for time-delay of linearly bidirectional coupled chaotic system

Based on Lyapunov stability theory and matrix measure, this paper presents a new generic criterion of global chaotic synchronization for bidirectional coupled chaotic system with time-delay. A new chaotic system with four-scroll attractor is chosen as an example to verify the effectiveness of the criterion. Numerical simulation are shown for demonstration.

Master–slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control

Global chaos synchronization of two identical non-autonomous horizontal platform systems coupled by linear state error feedback controller is investigated. The sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time-varied systems and Lyapunov's direct method, of which, the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices. In the examples, the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified. It is analytically and numerically examined that the synchronization criteria based on Lyapunov's direct method are sharper than the criteria based on the stability theory of linear time-varied systems.

Robust impulsive synchronization of uncertain dynamical networks

This paper studies robust impulsive synchronization of uncertain dynamical networks. By utilizing the concept of impulsive control and the stability results for impulsive systems, several criteria for robust local and robust global impulsive synchronization are established for complex dynamical networks, in which the network coupling functions are unknown but bounded. Three examples are also worked through for illustrating the main results.

Delay-dependent stability criteria for coupled chaotic systems via unidirectional linear error feedback approach☆

Abstract Based on the Lyapunov stability theory, matrix measure, and linear matrix inequality (LMI), this paper proposes some simple generic criteria for delay-dependent global synchronization between two coupled chaotic systems from a unidirectional linear error feedback coupling approach. A numerical example is discussed to illustrate our result.

Global synchronization criteria with channel time-delay for chaotic time-delay system

Based on the Lyapunov stabilization theory, matrix measure, and linear matrix inequality (LMIs), this paper studies the chaos synchronization of time-delay system using the unidirectional linear error feedback coupling with time-delay. Some generic conditions of chaos synchronization with time-delay in the transmission channel is established. The chaotic Chua’s circuit is used for illustration, where the coupling parameters are determined according to the criteria under which the global chaos synchronization of the time-delay coupled systems is achieved.

Global chaos synchronization with channel time-delay

This paper addresses a practical issue in chaos synchronization where there is a time-delay in the receiver as compared with the transmitter. A new synchronization scheme and a general criterion for global chaos synchronization are proposed and developed from the approach of unidirectional linear error feedback coupling with time-delay. The chaotic Chua’s circuit is used for illustration, where the coupling parameters are determined according to the criterion under which the global chaos synchronization of the time-delay coupled systems is achieved.

Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling

There are, in general, two classes of results regarding the synchronization of chaos in an array of coupled identical chaotic systems. The first class of results relies on Lyapunov's direct method and gives analytical criteria for global or local synchronization. The second class of results relies on linearization around the synchronization manifold and the computation of Lyapunov exponents. The computation of Lyapunov exponents is mainly done via numerical experiments and can only show local synchronization in the neighborhood of the synchronization manifold. On the other hand, Lyapunov's direct method is more rigorous and can give global results. The coupling topology is generally expressed in matrix form and the first class of methods mainly deals with symmetric matrices whereas the second class of methods can work with all diagonalizable matrices. The purpose of this brief is to bridge the gap in the applicability of the two classes of methods by considering the nonsymmetric case for the first class of methods. We derive a synchronization criterion for nonreciprocal coupling related to a numerical quantity that depends on the coupling topology and we present methods for computing this quantity.

A GLOBAL SYNCHRONIZATION CRITERION FOR COUPLED CHAOTIC SYSTEMS VIA UNIDIRECTIONAL LINEAR ERROR FEEDBACK APPROACH

Based on Lyapunov stabilization theory, this paper proposes a new generic criterion of global chaos synchronization between two coupled chaotic systems from a unidirectional linear error feedback coupling approach. The criterion is successfully applied to some typical chaotic systems with different types of nonlinearity, such as the classic Chua's circuit, the modified Chua's circuit with a sine function, and the Rössler and Lorenz chaotic systems. The coupling parameters are determined according to the new criterion so as to ensure the coupled systems' global chaos synchronization.