Find in Library

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.