Abstract
In this study, it is proposed that a new matrix projective synchronization of fractional-order (FO) chaotic maps in discrete-time. A new synchronization error is introduced and a control law is constructed, which makes the synchronization error converge towards zero in sufficient time under the stability theory of linearization method of FO systems. Numerical simulation results are presented to illustrate the feasibility of the scheme. Finally, a secure communication scheme based on FO discrete-time (FODT) systems was proposed.
Highlights
Chaos theory, in nonlinear dynamical systems, is a very attractive phenomenon, which has been extensively investigated and studied in the last decades
Since Pecora and Carroll proposed the complete synchronization method of chaotic system in 1990s, great strides have been made in chaotic synchronization [23,24,25,26,27,28,29,30,31]
In 2014, Hu [32] studied FO Henon map, which has made an unprecedented contribution to the high dimensional FO discrete-time (FODT) chaotic synchronization method
Summary
In nonlinear dynamical systems, is a very attractive phenomenon, which has been extensively investigated and studied in the last decades. In 2017, Shukla [34] studied generalized FO Henon map and proposed active control synchronization, and this synchronization method is only suitable for master-slave systems with the same dimension. Ouannas [35] proposed a general synchronization of FODT chaotic systems in 2018 Though this synchronization method can be suitable for master-slave systems with different dimensions, it's hard to find the right bijection function f to meet requirement. In order to better synchronize FODT chaotic systems with different dimensions, a new matrix projective synchronization, in this paper, is proposed. This new synchronization method relies on an invertible matrix P and VOLUME XX, 2017.
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