Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles - Novaes, Douglas D; Rondón, Gabriel [UNESP] (IOP Publishing, 2021)
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.
Keywords: blow-up method; boundary limit cycles; Fenichel theory; nonsmooth differential systems; regularization; tangential singularities