Abstract
In this paper, we study limit cycle bifurcations for planar piecewise smooth near-Hamiltonian systems with nth-order polynomial perturbation. The piecewise smooth linear differential systems with two centers formed in two ways, one is that a center-fold point at the origin, the other is a center-fold at the origin and another unique center point exists. We first explore the expression of the first order Melnikov function. Then by using the Melnikov function method, we give estimations of the number of limit cycles bifurcating from the period annulus. For the latter case, the simultaneous occurrence of limit cycles near both sides of the homoclinic loop is partially addressed.
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Acknowledgements
The authors of the paper would like to thank the reviewers and the handling editor for their insightful and valuable suggestions which improve greatly the presentation of the paper. The work is supported by the National Natural Science Foundation of China (Grant No.11931016).
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Chen, J., Han, M. Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System. Qual. Theory Dyn. Syst. 21, 34 (2022). https://doi.org/10.1007/s12346-022-00567-0
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DOI: https://doi.org/10.1007/s12346-022-00567-0