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arXiv · 1504.05459

Construction of heteroclinic networks in $\mathbb{R}^4$

Alexander Lohse·Sofia B. S. D. Castro
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Abstract

We study heteroclinic networks in $\mathbb{R}^4$, made of a certain type of simple robust heteroclinic cycle. In simple cycles all the connections are of saddle-sink type in two-dimensional fixed-point spaces. We show that there exist only very few ways to join such cycles together in a network and provide the list of all possible such networks in $\mathbb{R}^4$. The networks involving simple heteroclinic cycles of type A are new in the literature and we describe the stability of the cycles in these networks: while the geometry of type A and type B networks is very similar, stability distinguishes them clearly.

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Alexander Lohse, Sofia B. S. D. Castro. 2016-10-20. Construction of heteroclinic networks in $\mathbb{R}^4$. https://doi.org/10.1088/0951-7715%2F29%2F12%2F3677

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