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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Chunli Zhang & Yangjie Gao & Junliang Yao & Fucai Qian, 2024. "Synchronization of Bidirectionally Coupled Fractional-Order Chaotic Systems with Unknown Time-Varying Parameter Disturbance in Different Dimensions," Mathematics, MDPI, vol. 12(17), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2775-:d:1473840
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    References listed on IDEAS

    as
    1. Nian, Fuzhong & Liu, Xinmeng & Zhang, Yaqiong, 2018. "Sliding mode synchronization of fractional-order complex chaotic system with parametric and external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 22-28.
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