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Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems

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Abstract

The main aim of this paper is to study the limit cycle bifurcations near the homoclinic cycle in the discontinuous systems. Based on the impoved Lin’s method, we establish the bifurcation equation, which presents the existence of limit cycles bifurcated from nonsmooth homoclinic cycles under perturbation. Furthermore, we give an example to support our conclusions. After solving a boundary value problem with numerical tools, we provide the exact parameter values for the system having a limit cycle.

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Acknowledgements

This work is partially funded by the National Natural Science Foundation of China under Grant No.11871022, and supported in part by Science and Technology Commission of Shanghai Municipality (No. 22DZ2229014).

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  1. School of Mathematical Sciences, Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, People’s Republic of China

    Duo Hua & Xingbo Liu

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  1. Duo Hua
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  2. Xingbo Liu
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Correspondence to Xingbo Liu.

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Hua, D., Liu, X. Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems. J Dyn Diff Equat (2024). https://doi.org/10.1007/s10884-024-10358-7

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