Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 36, Issue 7, Pages 3545-3601Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2016.36.3545
Keywords
Filippov systems; regularization; singular perturbation theory; asymptotic methods; bifurcations
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Funding
- Spanish MINECO-FEDER [MTM2012-31714]
- Catalan Grant [2014SGR504]
- Russian Scientific Foundation [14-41-00044]
- European Marie Curie Action
- Russian Science Foundation [14-41-00044] Funding Source: Russian Science Foundation
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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.
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