Abstract
In order to get the lower bound of the number of limit cycles for near-Hamiltonian systems, one often faces the difficulty in verifying the independence of the coefficients of some polynomials. The difficulty is mainly coming from the tedious iterative computation. In the present paper, we provide an approach to verify the independence which largely reduces calculation and illustrate this method by perturbing a piecewise smooth Hamiltonian system with a homoclinic loop. Using this method, we prove that the maximal number of limit cycles of this system is \(n+[\frac{n+1}{2}]\), and this bound can be reached.
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
Supported by National Natural Science Foundation of China(12161069,12071037); Ningxia Natural Science Foundation of China(2022AAC05044,2020AAC03264); Construction of First-class Disciplines of Higher Education of Ningxia (Pedagogy) (NXYLXK2021B10) and Scientific Research Program of Higher Education of Ningxia(NGY2020074).
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Yang, J., Zhao, L. Bifurcation of Limit Cycles of a Piecewise Smooth Hamiltonian System. Qual. Theory Dyn. Syst. 21, 142 (2022). https://doi.org/10.1007/s12346-022-00674-y
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DOI: https://doi.org/10.1007/s12346-022-00674-y