Connecting minimal chimeras and fully asymmetric chaotic attractors through equivariant pitchfork bifurcations
Adaptation and Self-Organizing Systems
2021-06-23 v1 Chaotic Dynamics
Abstract
Highly symmetric networks can exhibit partly symmetry-broken states, including clusters and chimera states, i.e., states of coexisting synchronized and unsynchronized elements. We address the permutation symmetry of four globally coupled Stuart-Landau oscillators and uncover an interconnected web of differently symmetric solutions. Among these are chaotic minimal chimeras that arise from periodic solutions in a period-doubling cascade, as well as fully asymmetric chaotic states arising similarly from periodic solutions. A backbone of equivariant pitchfork bifurcations mediate between the two cascades, culminating in equivariant pitchforks of chaotic attractors.
Keywords
Cite
@article{arxiv.2102.10138,
title = {Connecting minimal chimeras and fully asymmetric chaotic attractors through equivariant pitchfork bifurcations},
author = {Sindre W. Haugland and Katharina Krischer},
journal= {arXiv preprint arXiv:2102.10138},
year = {2021}
}
Comments
5 pages, 2 figures + Supplementary Information 3 pages, 2 figures