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Research Article | Open Access

Time-delayed feedback control for chaotic systems with coexisting attractors

Erxi Zhu1,2( )
College of Internet of Things Engineering, Jiangsu Vocational College of Information Technology, Wuxi 214153, China
College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
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Abstract

This study investigated the Hopf bifurcation of the equilibrium point of chaotic systems with coexisting attractors under the time-delayed feedback control. First, the equilibrium point and Hopf bifurcation of chaotic systems with coexisting attractors were analyzed. Second, the chaotic systems were controlled by time-delayed feedback, the transversality condition of Hopf bifurcation at the equilibrium point was discussed, and the time-delayed value of Hopf bifurcation at the equilibrium point was obtained. Lastly, the correctness of the theoretical analysis was verified by using the numerical results.

Keywords

coexisting attractorstime-delayed feedback controlHopf bifurcationtransverse condition
CLC number: 93B52

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 1088-1102
DOI: 10.3934/math.2024053

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Cite this article:
Zhu E. Time-delayed feedback control for chaotic systems with coexisting attractors. AIMS Mathematics, 2024, 9(1): 1088-1102. https://doi.org/10.3934/math.2024053

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Received: 04 October 2023
Revised: 18 November 2023
Accepted: 27 November 2023
Published: 15 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)