Coupled Networks, Patterns and Complexity - Abstract
Maistrenko, Yuri
Chimera states are remarkable spatiotemporal patterns of coexisting phase-locked and drifting oscillators, which arise in arrays of coupled identical oscillators moreover, without any sign of asymmetry - as a manifestation of internal nonlinear nature of the model. We report the appearance of chimera states for repulsively coupled phase oscillators of the Kuramoto-Sakaguchi type, i.e. when phase lag $alpha > pi/2$. Then, the network coupling works against synchronization producing so-called q-twisted and multi-twisted states. We show that in this case, a variety of chimera states exists in a wide domain of the parameter space as a cascade with increasing number of the regions of irregularity (chimeras heads). We find that chimera states for the repulsively coupled phase oscillators grow from the multi-twisted states, and report three typical scenarios of the chimera birth: newline 1) via saddle-node bifurcation on an invariant circle, also known as SNIC or SNIPER, newline 2) via blue-sky catastrophe, when two periodic orbits - stable and saddle - approach each other creating a saddle-node periodic orbit, and newline 3) via more involved, homoclinic transition characterized by complex multistable network linebreak dynamics.