Stability of spiral chimera states on a torus. (English) Zbl 1386.37047
Summary: We study destabilization mechanisms of spiral coherence-incoherence patterns known as spiral chimera states that form on a two-dimensional lattice of nonlocally coupled phase oscillators. For this purpose we employ the linearization of the Ott-Antonsen equation that is valid in the continuum limit and perform a detailed two-parameter stability analysis of a \(D_4\)-symmetric chimera state, i.e., a four-core spiral state. We identify fold, Hopf, and parity-breaking bifurcations as the main mechanisms whereby spiral chimeras can lose stability. Beyond these bifurcations we find new spatio-temporal patterns, in particular quasiperiodic chimeras and \(D_2\)-symmetric spiral chimeras, as well as drifting states.
MSC:
| 37G35 | Dynamical aspects of attractors and their bifurcations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 35B36 | Pattern formations in context of PDEs |
| 34A33 | Ordinary lattice differential equations |
| 37L60 | Lattice dynamics and infinite-dimensional dissipative dynamical systems |
| 76F20 | Dynamical systems approach to turbulence |
Keywords:
coupled oscillators; coherence-incoherence patterns; chimera states; Ott-Antonsen equation; bifurcation analysisReferences:
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