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arXiv · 1606.02592

Stability of quasi-simple heteroclinic cycles

Liliana Garrido-da-Silva·Sofia B. S. D. Castro
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Abstract

The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose connections are 1-dimensional and contained in flow-invariant spaces of equal dimension. These heteroclinic cycles exist both in symmetric and non-symmetric contexts. We make one assumption on the dynamics along the connections to ensure that the transition matrices have a convenient form. Our method applies to all simple heteroclinic cycles of type Z and to various heteroclinic cycles arising in population dynamics, namely non-simple heteroclinic cycles, as well as to cycles that are part of a heteroclinic network. We illustrate our results with a non-simple cycle present in a heteroclinic network of the Rock-Scissors-Paper game.

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Liliana Garrido-da-Silva, Sofia B. S. D. Castro. 2016-06-08. Stability of quasi-simple heteroclinic cycles. https://arxiv.org/abs/1606.02592

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