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arXiv · 1707.08162

The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems

Douglas Duarte Novaes·Marco Antonio Teixeira·Iris de Oliveira Zeli
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Abstract

Generic bifurcation theory was classically well developed for smooth differential systems, establishing results for $k$-parameter families of planar vector fields. In the present study we focus on a qualitative analysis of $2$-parameter families, $Z_{\alpha,\beta}$, of planar Filippov systems assuming that $Z_{0,0}$ presents a codimension-two minimal set. Such object, named elementary simple two-fold cycle, is characterized by a regular trajectory connecting a visible two-fold singularity to itself, for which the second derivative of the first return map is nonvanishing. We analyzed the codimension-two scenario through the exhibition of its bifurcation diagram.

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Douglas Duarte Novaes, Marco Antonio Teixeira, Iris de Oliveira Zeli. 2017-07-25. The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems. https://doi.org/10.1088/1361-6544/aaaaf7

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