Snaking bifurcations of localized patterns on ring lattices
Dynamical Systems
2021-06-11 v1 Classical Analysis and ODEs
Abstract
We study the structure of stationary patterns in bistable lattice dynamical systems posed on rings with a symmetric coupling structure in the regime of small coupling strength. We show that sparse coupling (for instance, nearest-neighbour or next-nearest-neighbour coupling) and all-to-all coupling lead to significantly different solution branches. In particular, sparse coupling leads to snaking branches with many saddle-node bifurcations, whilst all-to-all coupling leads to branches with six saddle nodes, regardless of the size of the number of nodes in the graph.
Cite
@article{arxiv.2105.02380,
title = {Snaking bifurcations of localized patterns on ring lattices},
author = {Moyi Tian and Jason J. Bramburger and Bjorn Sandstede},
journal= {arXiv preprint arXiv:2105.02380},
year = {2021}
}