On Structural Stability of 3D Filippov Systems: A Semi-Local Approach

The main purpose of this work is to provide a non-local approach to study aspects of structural stability of 3D Filippov systems. We introduce a notion of semi-local structural stability which detects when a piecewise smooth vector field is robust around the whole switching manifold and we give a co...

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Bibliographic Details
Main Authors Gomide, Otávio M. L, Teixeira, Marco A
Format Journal Article
LanguageEnglish
Published 20.08.2017
Subjects
Mathematics - Dynamical Systems
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Summary:The main purpose of this work is to provide a non-local approach to study aspects of structural stability of 3D Filippov systems. We introduce a notion of semi-local structural stability which detects when a piecewise smooth vector field is robust around the whole switching manifold and we give a complete characterization of such systems. In particular, we present some methods in the qualitative theory of piecewise smooth vector fields, emphasizing a geometrical analysis of the foliations generated by their orbits. Such approach displays surprisingly a rich dynamical behaviour that has been studied in details in this work. It is worth to say that this subject has not been treated recently from a non-local point of view, and we hope that the approach adopted in this work contributes to the understanding of the structural stability for piecewise-smooth vector fields in its most global sense.
DOI:10.48550/arxiv.1708.05989