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arXiv · 1905.11950

Bifurcation Diagrams of Global Connections in Filippov Systems

Kamila S. Andrade·Otávio M. L. Gomide·Douglas D. Novaes
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Abstract

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.

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Kamila S. Andrade, Otávio M. L. Gomide, Douglas D. Novaes. 2019-05-28. Bifurcation Diagrams of Global Connections in Filippov Systems. https://doi.org/10.1016/j.nahs.2023.101397

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