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Periodic orbits for 2n-dimensional control piecewise smooth dynamical systems

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Abstract

In this paper we study the periodic orbits of a class of 2n-dimensional control dynamical systems with a perturbation of continuous piecewise smooth quadratic polynomial and a perturbation of discontinuous piecewise smooth polynomial of an arbitrarily given degree, respectively. By applying the averaging theory for continuous and discontinuous piecewise smooth systems, the number of isolated zeros of the averaging function can be determined, which provides a lower bound of the maximum number of isolated periodic orbits. At last, we give examples to show that the lower bound of the maximum number is accessible by the properties of algebraic closure and transcendental extension.

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Acknowledgements

The work is supported by the National Natural Science Foundation of China (Nos. 11931016, 12271355, 12161131001).

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Authors and Affiliations

  1. School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Chen Cao & Yilei Tang

  2. Science and Technology on Information System Engineering Laboratory, No.1 Lingshan South Road, Qixia District, Nanjing, 210007, People’s Republic of China

    Chen Fu

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  1. Chen Cao
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  2. Chen Fu
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  3. Yilei Tang
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Correspondence to Yilei Tang.

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Communicated by Huaizhong Zhao.

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Cao, C., Fu, C. & Tang, Y. Periodic orbits for 2n-dimensional control piecewise smooth dynamical systems. Comp. Appl. Math. 43, 260 (2024). https://doi.org/10.1007/s40314-024-02663-0

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  • DOI: https://doi.org/10.1007/s40314-024-02663-0

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