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Limit Cycle Bifurcations from a Quadratic Center with Two Switching Lines

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Abstract

In this paper, we study limit cycle bifurcations for a differential system with two switching lines by using Picard–Fuchs equation. We obtain a detailed expression of the corresponding first order Melnikov function which can be used to get the upper bound of the number of limit cycles. It is worth noting that we greatly simplify the computation. Our results also show that the number of switching lines has essential impact on the number of limit cycles bifurcating from a period annulus.

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Acknowledgements

Supported by National Natural Science Foundation of China (11701306, 11671040, 11601250), Construction of First-class Disciplines of Higher Education of Ningxia (Pedagogy)(NXYLXK2017B11), Young Top-notch Talent of Ningxia, Ningxia Natural Science Foundation of China (2019AAC03247) and Key Program of Ningxia Normal University (NXSFZDA1901).

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  1. School of Mathematics and Computer Science, Ningxia Normal University, Guyuan, 756000, China

    Jihua Yang

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  1. Jihua Yang
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Correspondence to Jihua Yang.

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Yang, J. Limit Cycle Bifurcations from a Quadratic Center with Two Switching Lines. Qual. Theory Dyn. Syst. 19, 21 (2020). https://doi.org/10.1007/s12346-020-00374-5

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