Limit Cycle Bifurcations from a Quadratic Center with Two Switching Lines

Abstract

In this paper, we study limit cycle bifurcations for a differential system with two switching lines by using Picard–Fuchs equation. We obtain a detailed expression of the corresponding first order Melnikov function which can be used to get the upper bound of the number of limit cycles. It is worth noting that we greatly simplify the computation. Our results also show that the number of switching lines has essential impact on the number of limit cycles bifurcating from a period annulus.