On the number of limit cycles in general planar piecewise linear systems of node–node types

Abstract

We investigate the existence and number of limit cycles in a class of general planar piecewise linear systems constituted by two linear subsystems with node–node dynamics. Using the Liénard-like canonical form with seven parameters, some sufficient and necessary conditions for the existence of limit cycles are given by studying the fixed points of proper Poincaré maps. In particular, we prove the existence of at least two nested limit cycles and describe some parameter regions where two limit cycles exist. The main results are applied to the PWL Morris–Lecar neural model to determine the existence and stability of the limit cycles.