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Symmetry
Volume 17
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10.3390/sym17060957
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Article

Novel Methods for Multi-Switch Generalized Projective Anti-Synchronization of Fractional Chaotic System Under Caputo–Fabrizio Derivative via Lyapunov Stability Theorem and Adaptive Control

by
Yu Zhao
2,
Tianzeng Li
2,
Yu Wang
1,* and
Rong Kang
2
1
School of Mathematics and Statistics, Hainan Normal University, Haikou 571127, China
2
School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(6), 957; https://doi.org/10.3390/sym17060957
Submission received: 22 April 2025 / Revised: 16 May 2025 / Accepted: 29 May 2025 / Published: 16 June 2025
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Abstract

The issue of multi-switch generalized projective anti-synchronization of fractional-order chaotic systems is investigated in this work. The model is constructed using Caputo–Fabrizio derivatives, which have been rarely addressed in previous research. In order to expand the symmetric and asymmetric synchronization modes of chaotic systems, we consider modeling chaotic systems under such fractional calculus definitions. Firstly, a new fractional-order differential inequality is proven, which facilitates the rapid confirmation of a suitable Lyapunov function. Secondly, an effective multi-switching controller is designed to confirm the convergence of the error system within a short moment to achieve synchronization asymptotically. Simultaneously, a multi-switching parameter adaptive principle is developed to appraise the uncertain parameters in the system. Finally, two simulation examples are presented to affirm the correctness and superiority of the introduced approach. It can be said that the symmetric properties of Caputo–Fabrizio fractional derivative are making outstanding contributions to the research on chaos synchronization.
Keywords: generalized projective synchronization; fractional chaotic system; unknown parameters; multi-switch generalized projective synchronization; fractional chaotic system; unknown parameters; multi-switch

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MDPI and ACS Style

Zhao, Y.; Li, T.; Wang, Y.; Kang, R. Novel Methods for Multi-Switch Generalized Projective Anti-Synchronization of Fractional Chaotic System Under Caputo–Fabrizio Derivative via Lyapunov Stability Theorem and Adaptive Control. Symmetry 2025, 17, 957. https://doi.org/10.3390/sym17060957

AMA Style

Zhao Y, Li T, Wang Y, Kang R. Novel Methods for Multi-Switch Generalized Projective Anti-Synchronization of Fractional Chaotic System Under Caputo–Fabrizio Derivative via Lyapunov Stability Theorem and Adaptive Control. Symmetry. 2025; 17(6):957. https://doi.org/10.3390/sym17060957

Chicago/Turabian Style

Zhao, Yu, Tianzeng Li, Yu Wang, and Rong Kang. 2025. "Novel Methods for Multi-Switch Generalized Projective Anti-Synchronization of Fractional Chaotic System Under Caputo–Fabrizio Derivative via Lyapunov Stability Theorem and Adaptive Control" Symmetry 17, no. 6: 957. https://doi.org/10.3390/sym17060957

APA Style

Zhao, Y., Li, T., Wang, Y., & Kang, R. (2025). Novel Methods for Multi-Switch Generalized Projective Anti-Synchronization of Fractional Chaotic System Under Caputo–Fabrizio Derivative via Lyapunov Stability Theorem and Adaptive Control. Symmetry, 17(6), 957. https://doi.org/10.3390/sym17060957

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