Abstract
Generalized synchronization of time-delayed fractional order chaotic systems is investigated. According to the stability theorem of linear fractional differential systems with multiple time-delays, a nonlinear fractional order controller is designed for the synchronization of systems with identical and non-identical derivative orders. Both complete synchronization and projective synchronization also can be realized based on the proposed controller. The effectiveness and robustness of the controller are verified in the numerical simulations.
Highlights
Chaos synchronization has been a hot subject in the field of nonlinear science due to its wide-scope potential applications in physical systems, biological science, chemical reactor, etc [1]
In 1995, Rulkov et al considered generalized synchronization, where the states of the response system synchronized with the map of the ones in the drive system [8]
Both complete synchronization and projective synchronization belong to generalized synchronization
Summary
Chaos synchronization has been a hot subject in the field of nonlinear science due to its wide-scope potential applications in physical systems, biological science, chemical reactor, etc [1]. It is difficult to make the drive and response systems achieve complete synchronization in the real applications. With the introduction of fractional derivative, chaotic synchronization of fractional order dynamical systems becomes an active research field due to its great potential applications especially in secure communication and control processing [16,17,18]. In 2015, Behinfaraz et al studied the modified projective synchronization of different fractional order chaotic systems with time-varying delays [34]. Motivated by the above discussion, the generalized synchronization of time-delayed fractional order chaotic systems is investigated in this work. The fractional order chaotic systems with or without time-delay can be used for achieving the generalized synchronization.
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