Journal
NONLINEAR DYNAMICS
Volume 73, Issue 3, Pages 1495-1505Publisher
SPRINGER
DOI: 10.1007/s11071-013-0880-1
Keywords
Synchronization; Anti-synchronization; Integer-order chaotic system; Fractional-order chaotic system; Takagi-Sugeno fuzzy
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Funding
- scientific research foundation of National Natural Science Foundation [51109180]
- National Science & Technology Supporting Plan from the Ministry of Science & Technology of China [2011BAD29B08]
- 111 Project from the Ministry of Education of P.R. of China
- State Administration of Foreign Experts Affairs of P.R. of China [B12007]
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In this study, we investigate a class of chaotic synchronization and anti-synchronization with stochastic parameters. A controller is composed of a compensation controller and a fuzzy controller which is designed based on fractional stability theory. Three typical examples, including the synchronization between an integer-order Chen system and a fractional-order Lu system, the anti-synchronization of different 4D fractional-order hyperchaotic systems with non-identical orders, and the synchronization between a 3D integer-order chaotic system and a 4D fractional-order hyperchaos system, are presented to illustrate the effectiveness of the controller. The numerical simulation results and theoretical analysis both demonstrate the effectiveness of the proposed approach. Overall, this study presents new insights concerning the concepts of synchronization and anti-synchronization, synchronization and control, the relationship of fractional and integer order nonlinear systems.
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