Stability of spiral chimera states on a torus
- Omel'chenko, Oleh E.
- Wolfrum, Matthias
- Knobloch, Edgar
2010 Mathematics Subject Classification
- 34C15 37G35 34D06 35B36
- Coupled oscillators, coherence-incoherence patterns, chimera states, Ott--Antonsen equation, bifurcation analysis
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, $D_2$-symmetric spiral chimeras as well as drifting states.
- SIAM J. Appl. Dyn. Syst., 17 (2018), pp. 97--127, DOI 10.1137/17M1141151 .