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Dynamic analysis of a strange novel chaotic fractional-order system with fully golden proportion equilibria

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Abstract

This paper is focused on a strange novel chaotic fractional-order system with fully golden proportion equilibria. By using the stability theory of fractional-order systems, we give sufficient conditions for local stability of such system around equilibrium point. And then we prove the conditions for the existence of Hopf bifurcation. Moreover, delayed feedback control method is used to control the chaotic behavior of system. The results indicate that the fractional system is more stable than the classical system, where the fractional order \(\alpha \) and time delay \(\tau \) play an important role in controlling the chaotic dynamics. Finally, by using Adams–Bashforth–Moulton method, we implement some simulations to substantiate the obtained theoretical results.

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Some or all data, models, or code generated or used during the study are available from the corresponding author by request.

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Funding

This work is supported by the National Natural Science Foundation of China (No. U1610253) and the Fund for Shanxi “1331 Project” Key Subjects Construction.

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Authors and Affiliations

  1. College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, China

    J-B Wang & L-F Ma

  2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, China

    J-K Liu

  3. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan, China

    J-B Wang & J-K Liu

Authors
  1. J-B Wang
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  2. L-F Ma
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  3. J-K Liu
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Contributions

J.B. Wang carried out the study. L.F. Ma supervised the work and provided the support of funds. All authors read and approved the final manuscript.

Corresponding author

Correspondence to L-F Ma.

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Wang, JB., Ma, LF. & Liu, JK. Dynamic analysis of a strange novel chaotic fractional-order system with fully golden proportion equilibria. Indian J Phys 96, 2907–2920 (2022). https://doi.org/10.1007/s12648-021-02214-x

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  • DOI: https://doi.org/10.1007/s12648-021-02214-x

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