Electron. J. Diff. Equ., Vol. 2015 (2015), No. 108, pp. 1-17.

Limit cycles for piecewise smooth perturbations of a cubic polynomial differential center

Shimin Li, Tiren Huang

Abstract:
In this article, we study the planar cubic polynomial differential system
$$\displaylines{ \dot{x}=-yR(x,y)\cr \dot{y}=xR(x,y) }$$
where $R(x,y)=0$ is a conic and $R(0,0)\neq 0$. We find a bound for the number of limit cycles which bifurcate from the period annulus of the center, under piecewise smooth cubic polynomial perturbations. Our results show that the piecewise smooth cubic system can have at least 1 more limit cycle than the smooth one.

Submitted October 24, 2014. Published April 21, 2015.
Math Subject Classifications: 34A36, 34C07, 37G15.
Key Words: Limit cycle; piecewise smooth system; averaging method.

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Shimin Li
School of Mathematics and Statistics
Guangdong University of Finance and Economics
Guangzhou 510320, China
email: lism1983@126.com
Tiren Huang
Department of Mathematics
Zhejiang Sci-Tech University
Hangzhou 310018, China
email: htiren@zstu.edu.cn

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