Dynamical analysis reveals sliding-saddle homoclinic orbits in three-dimensional Filippov systems, highlighting conditions where perturbations create new sliding cycles.
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.
No takes yet. Share an insight, caveat, or question.
Huan et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: