Chaos induced by sliding phenomena in Filippov systems

Abstract

In this paper we provide a full topological and ergodic description of the dynamics of Filippov systems nearby a sliding Shilnikov orbit. More specifically we prove that the first return map, defined nearby this orbit, is topologically conjugate to a Bernoulli shift with infinite topological entropy. In particular, we see that for each natural number m it has infinitely many periodic points with period m.

Cited by in corpus (5)

• Sliding Shilnikov Connection in Filippov-type Predator-Prey Model
• The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems
• Study of periodic orbits in periodic perturbations of planar reversible Filippov systems having a two-fold cycle
• A note on invariant measures for Filippov systems
• On the Hausdorff dimension and Cantor set structure of sliding Shilnikov invariant sets