Regularization of sliding global bifurcations derived from the local fold singularity of Filippov systems

Carles  Bonet-Revés; Tere  M-Seara

doi:10.3934/dcds.2016.36.3545

Article Contents

2016, Volume 36, Issue 7: 3545-3601. Doi: 10.3934/dcds.2016.36.3545

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Regularization of sliding global bifurcations derived from the local fold singularity of Filippov systems

Carles Bonet-Revés^1, and
Tere M-Seara^1,

1.
Dept. Matemàtiques, secció ETSEIB, UPC, Avda. Diagonal 647, Barcelona, 08028

Received: January 31, 2015

Revised: December 31, 2015

Published: May 2017

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Abstract

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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Mathematics Subject Classification: Primary: 34E15, 34E10; Secondary: 37G15, 37G10.

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