Abstract
This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results.
Highlights
In recent years, more and more attention has been diverted towards the study of fractionalorder chaotic systems due to their potential applications in the fields of secure communication, encryption, signal and control processing [1,2,3,4,5]
The objective of this paper is to find the suitable and effective controllers Ui (i = 1, 2, . . . , N – 1) such that the error dynamical system (4) is transformed into a nonlinear system with antisymmetric structure and asymptotically stable at the origin
5 Conclusions In this paper, we introduce, analyze, and validate synchronization of N -coupled fractionalorder chaotic systems with ring connection by utilizing the bidirectional coupling
Summary
More and more attention has been diverted towards the study of fractionalorder chaotic systems due to their potential applications in the fields of secure communication, encryption, signal and control processing [1,2,3,4,5]. Several different types of synchronization for fractional-order chaotic systems have been observed and developed in the previous works. As a special class of nonlinear systems, have been extensively studied in theoretical physics and other fields of natural sciences and engineering. Multiple chaotic systems can be coupled in a ring which makes them correlative. Synchronization of coupled chaotic systems with ring connection extends the traditional mode of
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