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“Connecting surfaces” can locate hidden attractors

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Abstract

Hidden attractors are often associated with rare or unusual oscillations in the system, potentially catastrophic hazards for structures such as bridges and aircraft. Due to the lack of reasonable analytical and numerical methods, locating them is one of the most challenging tasks in nonlinear dynamics. In previous work, several localization methods have some limitations, such as low localization efficiency, inaccurate localization, and small localization range. In this study, we observed a new class of critical points named jerk points, where the jerk is zero, but the velocity and acceleration remain non-zero. The results indicate that jerk points are very significant for comprehending the transient dynamics in the phase space. Based on the jerk points, we propose the connecting surface method, which is composed of a set of inflection points, including fixed points, perpetual points and jerk points. It provides as much potential information in system dynamics as possible and can capture attractors more comprehensively, especially multiple stable and hidden attractors. By comparing existing methods and considering various 3D dynamic systems, the results show that the proposed method is effective and superior. The method can be used in the general research of dynamic systems and has high localization efficiency and a wide search range in localization hiding and coexistence attractors.

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Acknowledgments

This work was supported by the National Natural Science Foundations of China under Grant Nos. 62071411 and 62171401.

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Authors and Affiliations

  1. School of Physics and Opotoelectric Engineering, Xiangtan University, Xiangtan, 411105, Hunan, China

    Wanye Song & Yicheng Zeng

  2. School of Automation and Electronic Information, Xiangtan University, Xiangtan, 411105, China

    Zhijun Li & Mengjiao Wang

Authors
  1. Wanye Song
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  2. Yicheng Zeng
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  3. Zhijun Li
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  4. Mengjiao Wang
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Contributions

WS, YZ, ZL and MW designed and performed the research as well as wrote the paper. The authors contributed equally to this work. All authors read and approved the final manuscript.

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Correspondence to Wanye Song.

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The authors have no conflicts to disclose.

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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Song, W., Zeng, Y., Li, Z. et al. “Connecting surfaces” can locate hidden attractors. Eur. Phys. J. Plus 138, 168 (2023). https://doi.org/10.1140/epjp/s13360-022-03588-5

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