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arXiv · 2102.10138

Connecting minimal chimeras and fully asymmetric chaotic attractors through equivariant pitchfork bifurcations

Sindre W. Haugland·Katharina Krischer
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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 $\mathbb{S}_4$ permutation symmetry of four globally coupled Stuart-Landau oscillators and uncover an interconnected web of differently symmetric solutions. Among these are chaotic $2\!-\!1\!-\!1$ minimal chimeras that arise from $2\!-\!1\!-\!1$ periodic solutions in a period-doubling cascade, as well as fully asymmetric chaotic states arising similarly from periodic $1\!-\!1\!-\!1\!-\!1$ solutions. A backbone of equivariant pitchfork bifurcations mediate between the two cascades, culminating in equivariant pitchforks of chaotic attractors.

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Sindre W. Haugland, Katharina Krischer. 2021-02-19. Connecting minimal chimeras and fully asymmetric chaotic attractors through equivariant pitchfork bifurcations. https://doi.org/10.1103/physreve.103.l060201

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