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Synchronization and antisynchronization of N ‐coupled fractional‐order complex chaotic systems with ring connection
Author(s) -
Jiang Cuimei,
Zhang Fangfang,
Li Tongxing
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4765
Subject(s) - mathematics , synchronization (alternating current) , fractional calculus , fractional order system , chaotic , antisymmetric relation , nonlinear system , connection (principal bundle) , synchronization of chaos , lyapunov function , order (exchange) , quadratic equation , stability (learning theory) , control theory (sociology) , topology (electrical circuits) , computer science , physics , geometry , control (management) , finance , combinatorics , quantum mechanics , artificial intelligence , machine learning , economics , mathematical physics
This paper is devoted to investigate synchronization and antisynchronization of N ‐coupled general fractional‐order complex chaotic systems described by a unified mathematical expression with ring connection. By means of the direct design method, the appropriate controllers are designed to transform the fractional‐order error dynamical system into a nonlinear system with antisymmetric structure. Thus, by using the recently established result for the Caputo fractional derivative of a quadratic function and a fractional‐order extension of the Lyapunov direct method, several stability criteria are derived to ensure the occurrence of synchronization and antisynchronization among N ‐coupled fractional‐order complex chaotic systems. Moreover, numerical simulations are performed to illustrate the effectiveness of the proposed design.