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Centers and isochronous centers of a class of quasi-analytic switching systems

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Abstract

Abstract In this paper, we study the integrability and linearization of a class of quadratic quasi-analytic switching systems. We improve an existing method to compute the focus values and periodic constants of quasi-analytic switching systems. In particular, with our method, we demonstrate that the dynamical behaviors of quasi-analytic switching systems are more complex than those of continuous quasi-analytic systems, by showing the existence of six and seven limit cycles in the neighborhood of the origin and infinity, respectively, in a quadratic quasi-analytic switching system. Moreover, explicit conditions are obtained for classifying the centers and isochronous centers of the system.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11371373 and 11601212), Applied Mathematics Enhancement Program of Linyi University and the Natural Science and Engineering Research Council of Canada (Grant No. R2686A02).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Linyi University, Linyi, 276005, China

    Feng Li & Yuanyuan Liu

  2. Department of Applied Mathematics, Western University, London, Ontario, N6A 5B7, Canada

    Pei Yu

  3. School of Mathematics and Statistics, Central South University, Changsha, 410012, China

    Yirong Liu

Authors
  1. Feng Li
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  2. Pei Yu
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  3. Yirong Liu
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  4. Yuanyuan Liu
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Corresponding author

Correspondence to Pei Yu.

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This paper has been posted on arXiv.org since August 24, 2017, No. 1708.07546

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Li, F., Yu, P., Liu, Y. et al. Centers and isochronous centers of a class of quasi-analytic switching systems. Sci. China Math. 61, 1201–1218 (2018). https://doi.org/10.1007/s11425-016-9158-2

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