Existence and Bifurcation of a New Type of Sliding Homoclinic Orbit in a Class of 3D-Filippov Systems with Two Zones

In this paper, we investigate the existence and bifurcation of a new type of sliding homoclinic orbit (which will be called sliding-saddle-type homoclinic orbit) connecting a sliding saddle to itself in a family of 3D-piecewise-linear differential systems with two zones. We provide some sufficient conditions for the existence of this new type of sliding homoclinic orbit and then give a concrete example. In addition, we obtain some sufficient conditions to guarantee that this type of sliding homoclinic orbit can give birth to a sliding cycle under small perturbations.