Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
Personal tools
Log in

MPI Advance

Monday, 17.09.2012 14 c.t.

Chimera states for repulsively coupled phase oscillators

by Prof. Yuri Maistrenko
from National Academy of Sciences of Ukraine, Kiev, Ukraine

Contact person: Marc Timme


Hörsaal Haus 8 (Bunsenstr.)


Chimera state represents a remarkable spatiotemporal patterns in which phase-locked oscillators coexist with drifting ones. A peculiarity of this type hybrid behavior is the following: It arises in arrays of coupled identical oscillators without any sign of asymmetry as a manifestation of an internal nonlinear nature of the dynamical networks. We report the appearance of the chimera states for a network of repulsively coupled phase oscillators of the Kuramoto-Sakaguchi type (...) where the phase shift α> π/2, i.e., when the coupling works against phase synchronization of the oscillators producing splay states or q-twisted states. We show that depending on the phase shift α and the coupling radius r=P/N the network dynamics can be much more complicated compare to the model with the attractive coupling (α< π/2). In particular, chimera states can typically appear in a wide domain of the parameter space moreover, as a cascade of the states with increasing number of the regions of irregularity. We find that chimera states for the repulsively coupled phase oscillators grow from the so-called multi-twisted states. We report three scenarios of the chimera birth: 1) via saddle-node bifurcation on invariant circle, also known as SNIC or SNIPER, 2) via blue-sky catastrophe, when two periodic orbits – stable and saddle - approach each other creating the saddle-node periodic orbit, and 3) in more complicated, homoclinic scenario, when the unstable manifold may come back crossing the stable manifold of the saddle-node.

back to overview