Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle–focus type

Abstract

Abstract The aim of this paper is to deal with the problem of limit cycles for a general planar piecewise linear differential system of saddle–focus type. By using the Lienard-like canonical form with five parameters and dividing the total parameter space into several regions, the number of limit cycles is discussed in detail. In particular, we give parameter regions where there are at least two limit cycles. Moreover, we investigate the existence and stability of exactly two nested limit cycles in some parameter regions.