Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles

Abstract

Understanding how tangential singularities evolve under smoothing processes was one of the first problem concerning regularization of Filippov systems. In this paper, we are interested in $C^n$-regularizations of Filippov systems around visible regular-tangential singularities of even multiplicity. More specifically, using Fenichel Theory and Blow-up Methods, we aim to understand how the trajectories of the regularized system transits through the region of regularization. We apply our results to investigate $C^n$-regularizations of boundary limit cycles with even multiplicity contact with the switching manifold.

Cited by in corpus (5)

• Lyapunov coefficients for monodromic tangential singularities in Filippov vector fields
• Bifurcation Diagrams of Global Connections in Filippov Systems
• Sliding mode on tangential sets of Filippov systems
• On the non-existence of isochronous tangential centers in Filippov vector fields
• On the stability of hybrid polycycles