Abstract

We provide for a three parametric family of continuous piecewise linear differential systems an analytical proof on the existence of a two parametric family of homoclinic orbits. These homoclinic orbits there exist both under Shil′nikov () and non--Shil′nikov ($1\; \le \; \delta$) assumptions. As it is well know, under Shil′nikov assumptions there exist infinitely many periodic orbits accumulating to the homoclinic loop. Wealso prove that this behaviour persist at $\delta =1$. Moreover, a description of a possible evolution of such periodic orbits for $1\; \le \; \delta$ is presented.