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Periodic solutions and circuit design of chaos in a unified stretch-twist-fold flow

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Abstract

Based on the original stretch-twist-fold flow, we propose a unified stretch–twist–fold (USTF) flow. We explore the conditions that zero-Hopf bifurcation occurs at the origin. Using the first-order averaging theorem, a periodic solution produced from the zero-Hopf equilibrium is derived. In addition, we obtain the conclusion that for parameter \(\alpha \) large enough, the periodic orbit of USTF flow exists as well unstable. Finally, circuit design has been built for implementing the new system, showing a good agreement between computer simulations and experimental observations.

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Data Availability Statement

My manuscript has no associated data or the data will not be deposited. \(\ldots \).

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Acknowledgements

We thank the editors and referees for their comments which helped us improve the presentation of this paper. This work was supported by the National Natural Science Foundation of China (No. 11772306), Zhejiang Provincial Natural Science Foundation of China under Grant (No. LY20A020001), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (CUGGC05).

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Authors and Affiliations

  1. School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan, 430074, China

    Chenhua Li & Zhouchao Wei

  2. Zhejiang Institute, China University of Geosciences, Hangzhou, 311305, Zhejiang, China

    Zhouchao Wei

  3. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China

    Wei Zhang

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  1. Chenhua Li
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  2. Zhouchao Wei
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  3. Wei Zhang
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Correspondence to Zhouchao Wei.

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Li, C., Wei, Z. & Zhang, W. Periodic solutions and circuit design of chaos in a unified stretch-twist-fold flow. Eur. Phys. J. Spec. Top. 230, 1971–1978 (2021). https://doi.org/10.1140/epjs/s11734-021-00127-8

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