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Coexistence of singular cycles in a class of three-dimensional piecewise affine systems

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Abstract

Singular cycles (homoclinic orbits and heteroclinic cycles) play an important role in the study of chaotic dynamics of dynamical systems. This paper provides the coexistence of singular cycles that intersect the switching manifold transversely at two points in a class of three-dimensional two-zone piecewise affine systems. Moreover, the switching manifold of the systems is constructed by two perpendicular planes. Different to the three-dimensional piecewise affine systems with a switching plane, the system can ensure the coexistence of two homoclinic orbits to the same one equilibrium point and two heteroclinic cycles constructing by three heteroclinic orbits. In addition, three examples with simulations of the singular cycles are provided to illustrate the effectiveness of the results.

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Acknowledgements

The authors thank editors and referees for their kind careful review and valuable suggestions. This work is supported by National Natural Science Foundation of China (11801329), Natural Science Foundation of Shandong province (ZR2018BA002) and the University Natural Sciences Research Project of Anhui Province (KJ2021A0996).

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  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Minghao Liu, Ruimin Liu & Tiantian Wu

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  1. Minghao Liu
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  2. Ruimin Liu
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  3. Tiantian Wu
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Correspondence to Tiantian Wu.

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Liu, M., Liu, R. & Wu, T. Coexistence of singular cycles in a class of three-dimensional piecewise affine systems. Comp. Appl. Math. 43, 292 (2024). https://doi.org/10.1007/s40314-024-02824-1

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