Bifurcation diagrams of global connections in Filippov systems

In this paper, we are concerned about the qualitative behavior of planar Filippov systems around some typical invariant sets, namely, polycycles. In the smooth context, a polycycle is a simple closed curve composed by a collection of singularities and regular orbits, inducing a first return map. Her...

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Bibliographic Details
Published inNonlinear analysis. Hybrid systems Vol. 50; p. 101397
Main Authors Andrade, Kamila S., Gomide, Otávio M.L., Novaes, Douglas D.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.11.2023
Subjects
Bifurcation theory
Filippov system
Piecewise smooth differential system
Polycycle
Regular-tangential singularity
Piecewise smooth differential system
34C37
34A36
34C23
Polycycle
Bifurcation theory
Filippov system
Regular-tangential singularity
37G15
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Summary:In this paper, we are concerned about the qualitative behavior of planar Filippov systems around some typical invariant sets, namely, polycycles. In the smooth context, a polycycle is a simple closed curve composed by a collection of singularities and regular orbits, inducing a first return map. Here, this concept is extended to Filippov systems by allowing typical Filippov singularities lying on the switching manifold. Our main goal consists in developing a method to investigate the unfolding of polycycles in Filippov systems. In addition, we apply this method to describe bifurcation diagrams of Filippov systems around certain polycycles.
ISSN:1751-570X
DOI:10.1016/j.nahs.2023.101397