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arXiv · 2105.10757

Periodic forcing of a heteroclinic network

Isabel S. Labouriau·Alexandre A. P. Rodrigues
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Abstract

We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential equations defining a flow on a three-dimensional manifold. When both parameters are zero, its flow exhibits an attracting heteroclinic network associated to two periodic solutions. After slightly increasing both parameters, while keeping a two-dimensional connection unaltered, we focus our attention in the case where the two-dimensional invariant manifolds of the periodic solutions do not intersect. We prove a wide range of dynamical behaviour, ranging from an attracting quasi-periodic torus to rotational horseshoes and H\'enon-like strange attractors. We illustrate our results with an explicit example.

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Isabel S. Labouriau, Alexandre A. P. Rodrigues. 2021-05-22. Periodic forcing of a heteroclinic network. https://arxiv.org/abs/2105.10757

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