Synchronization of Bidirectionally Coupled Fractional-Order Chaotic Systems with Unknown Time-Varying Parameter Disturbance in Different Dimensions

Chunli Zhang, Yangjie Gao, Junliang Yao () and Fucai Qian
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Chunli Zhang: Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi’an University of Technology, Xi’an 710048, China
Yangjie Gao: Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi’an University of Technology, Xi’an 710048, China
Junliang Yao: Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi’an University of Technology, Xi’an 710048, China
Fucai Qian: Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi’an University of Technology, Xi’an 710048, China

Mathematics, 2024, vol. 12, issue 17, 1-16

Abstract: In this article, the synchronization of bidirectionally coupled fractional-order chaotic systems with unknown time-varying parameter disturbance in different dimensions is investigated. The scale matrices are designed to address the problem of the synchronization for fractional-order chaotic systems across two different dimensions. Congelation of variables is used to deal with the unknown time-varying parameter disturbance. Based on Lyapunov’s stability theorem, the synchronization controllers in different dimensions are obtained. At the same time, adaptive laws of the unknown disturbance can be designed. Benefiting from the proposed methods, we verify all the synchronization errors can converge to zero as time approaches infinity, regardless of whether in n-D or m-D synchronization, simultaneously ensuring that both control and estimation signals are bounded. Finally, simulation studies based on fractional-order financial systems are carried out to validate the effectiveness of the proposed synchronization method.

Keywords: fractional-order; chaotic synchronization; bidirectionally coupled; scale matrices; synchronization in different dimensions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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