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Limit Cycle Bifurcations in Perturbations of a Reversible Quadratic System with a Non-rational First Integral

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Abstract

This paper investigates the Hopf cyclicity of a piecewise smooth quadratic polynomial system by Melnikov function method, whose unperturbed system is a concrete reversible quadratic system with a center at the origin and with a non-rational first integral. By comparing the obtained result for the piecewise case with the result for the smooth case, it shows that the piecewise system can have at least four more limit cycles around the origin than the smooth one.

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Acknowledgements

We would like to thank the referee and the Editor for their valuable suggestions which helped to improve the presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Yanqin Xiong & Rong Cheng

  2. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, China

    Na Li

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  1. Yanqin Xiong
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  2. Rong Cheng
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  3. Na Li
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Correspondence to Yanqin Xiong.

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The first author was supported by National Natural Science Foundation of China (11701289, 11501055) and Natural Science Foundation of Jiangsu Province (BK20170936).

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Xiong, Y., Cheng, R. & Li, N. Limit Cycle Bifurcations in Perturbations of a Reversible Quadratic System with a Non-rational First Integral. Qual. Theory Dyn. Syst. 19, 97 (2020). https://doi.org/10.1007/s12346-020-00434-w

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  • DOI: https://doi.org/10.1007/s12346-020-00434-w

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