Chimera patterns in the Kuramoto-Battogtokh model

Abstract

Kuramoto and Battogtokh [Nonlinear Phenom. Complex Syst. 5, 380 (2002)] discovered chimera states represented by stable coexisting synchrony and asynchrony domains in a lattice of coupled oscillators. After reformulation in terms of local order parameter, the problem can be reduced to partial differential equations. We find uniformly rotating periodic in space chimera patterns as solutions of a reversible ordinary differential equation, and demonstrate a plethora of such states. In the limit of neutral coupling they reduce to analytical solutions in form of one- and two-point chimera patterns as well as localized chimera solitons. Patterns at weakly attracting coupling are characterized by virtue of a perturbative approach. Stability analysis reveals that only simplest chimeras with one synchronous region are stable.

5 pages, 6 figures

References in corpus (4)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Chimeras in networks with purely local coupling

Cited by in corpus (10)

• Breathing multichimera states in nonlocally coupled phase oscillators
• Pattern selection in a ring of Kuramoto oscillators
• Stability of rotatory solitary states in Kuramoto networks with inertia
• Locking and regularisation of chimeras by periodic forcing
• Emergence of second coherent regions for breathing chimera states
• Solitary synchronization waves in distributed oscillators populations
• Circular Cumulant Reductions for Macroscopic Dynamics of Kuramoto Ensemble with Multiplicative Intrinsic Noise
• Variety of rotation modes in a small chain of coupled pendulums
• Finite-density-induced motility and turbulence of chimera solitons
• Collective in-plane magnetization in a 2D XY macrospin system within the framework of generalized Ott-Antonsen theory