English

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 S4\mathbb{S}_4 permutation symmetry of four globally coupled Stuart-Landau oscillators and uncover an interconnected web of differently symmetric solutions. Among these are chaotic 2 ⁣ ⁣1 ⁣ ⁣12\!-\!1\!-\!1 minimal chimeras that arise from 2 ⁣ ⁣1 ⁣ ⁣12\!-\!1\!-\!1 periodic solutions in a period-doubling cascade, as well as fully asymmetric chaotic states arising similarly from periodic 1 ⁣ ⁣1 ⁣ ⁣1 ⁣ ⁣11\!-\!1\!-\!1\!-\!1 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