Open AccessRegularization of sliding global bifurcations derived from the local fold singularity of Filippov systems
Author(s) -
Carles Bonet-Revés,
Tere M. Seara
Publication year - 2016
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2016.36.3545
Subject(s) - homoclinic orbit , regularization (linguistics) , singularity , mathematics , fold (higher order function) , planar , mathematical analysis , nonlinear system , bifurcation , physics , computer science , artificial intelligence , programming language , computer graphics (images) , quantum mechanics
In this paper we study the Sotomayor-Teixeira regularization of a general visible fold singularity of a planar Filippov system. Extending Geometric Fenichel Theory beyond the fold with asymptotic methods, we determine the deviation of the orbits of the regularized system from the generalized solutions of the Filippov one. This result is applied to the regularization of global sliding bifurcations as the Grazing-Sliding of periodic orbits and the Sliding Homoclinic to a Saddle, as well as to some classical problems in dry friction.; Roughly speaking, we see that locally, and also globally, the regularization of the bifurcations preserve the topological features of the sliding ones.Peer ReviewedPostprint (author's final draft