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arXiv · 2309.12246

Bistable boundary conditions implying codimension 2 bifurcations

David A Rand·Meritxell Saez
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Abstract

We consider generic families $X_\param$ of smooth dynamical systems depending on parameters $\param\in P$ where $P$ is a 2-dimensional simply connected domain and assume that each $X_\param$ only has a finite number of restpoints and periodic orbits. We prove that if over the boundary of $P$ there is a S or Z shaped bifurcation graph containing two opposing fold bifurcation points while over the rest of the boundary there are no other bifurcation points, then, if there is no fold-Hopf bifurcation in $P$ then there is at least one cusp in the interior of $P$.

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David A Rand, Meritxell Saez. 2023-09-21. Bistable boundary conditions implying codimension 2 bifurcations. https://arxiv.org/abs/2309.12246

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