Crossing Limit Cycles in Planar Piecewise Linear Systems Separated by a Nonregular Line with Node–Node Type Critical Points

Abstract

In this paper, we investigate the existence and number of crossing limit cycles in a class of planar piecewise linear systems with node–node type critical points defined in two zones separated by a nonregular line formed by two rays emanated from the origin $(0,0)$, which are the positive $x$- and $y$-axes. We focus our attention on the existence of two-point crossing limit cycles, which intersect the switching line at two points. We obtain sufficient conditions under which the system has two two-point crossing limit cycles which intersect only one of the two rays. Moreover, we construct examples to show that this class of systems can have two, three or four two-point crossing limit cycles.