Chaos in Coupled Heteroclinic Cycles and its Piecewise-Constant Representation
Abstract
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of coupling. With increase of coupling strength, several symmetry-changing transitions are observed, and finally a stable periodic orbit appears via an inverse period-doubling cascade. To reveal the behavior at extremely small couplings, a piecewise-constant model for the dynamics is suggested. Within this model we construct a Poincar\'e map for a chaotic state numerically, it appears to be an expanding non-invertable circle map thus confirming abundance of chaos in the small coupling limit. We also show that within the piecewise-constant description, there is a set of periodic solutions with different phase shifts between subsystems, due to dead zones in the coupling.
Keywords
Cite
@article{arxiv.2202.00288,
title = {Chaos in Coupled Heteroclinic Cycles and its Piecewise-Constant Representation},
author = {Arkady Pikovsky and Alexander Nepomnyashchy},
journal= {arXiv preprint arXiv:2202.00288},
year = {2023}
}