Jiaxin Wang, Liqin Zhao
Published 2021-08-23Version 1
In this paper, we study the bifurcate of limit cycles for Bogdanov-Takens system($\dot{x}=y$, $\dot{y}=-x+x^{2}$) under perturbations of piecewise smooth polynomials of degree $2$ and $n$ respectively. We bound the number of zeros of first order Melnikov function which controls the number of limit cycles bifurcating from the center. It is proved that the upper bounds of the number of limit cycles with switching curve $x=y^{2m}$($m$ is a positive integral) are $(39m+36)n+77m+21(m\geq 2)$ and $50n+52(m=1)$ (taking into account the multiplicity). The upper bounds number of limit cycles with switching lines $x=0$ and $y=0$ are 11 (taking into account the multiplicity) and it can be reached.
On the number of limit cycles for generic Lotka-Volterra system and Bogdanov-Takens system under perturbations of piecewise smooth polynomials
Detecting the limit cycles for a class of Hamiltonian systems under thirteen-order perturbed terms
On the number of limit cycles for polycycles $S^{(2)}$ and $S^{(3)}$ in quadratic Hamilton systems under perturbations of piecewise smooth polynomials
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