Limit cycles in a switching Liénard system

Abstract

<p style='text-indent:20px;'>In this paper, we consider a class of quadratic switching Liénard systems with three switching lines. We give an algorithm for computing the Lyapunov constants of this system. Based on this method, we obtain a center condition and three limit cycles bifurcating from the focus <inline-formula><tex-math id="M1">\begin{document}$ (0,0) $\end{document}</tex-math></inline-formula>. Further, an example of quadratic switching systems is constructed to show the existence of six limit cycles bifurcating from the center. This is a new low bound on the maximal number of small-amplitude limit cycles obtained in such quadratic switching systems.</p>