Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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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

Location

Hörsaal Haus 8 (Bunsenstr.)

Abstract

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.

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