Chimera patterns in one-dimensional oscillatory medium

Abstract

Kuramoto and Battogtokh [Nonlinear Phenom. Complex Syst. 5, 380 (2002)] described chimera states as a coexistence of synchrony and asynchrony in a one-dimensional oscillatory medium. After a reformulation in terms of a local complex order parameter, the problem can be reduced to a system of partial differential equations.We further reduce finding of uniformly rotating, spatially periodic chimera patterns to solving a reversible ordinary differential equation, and demonstrate that the latter has many solutions. In the limit of neutral coupling, analytical solutions in the form of one- and two-point chimera patterns as well as localized chimera solitons are found. Based on these analytic results, patterns at weakly attracting coupling are characterized by virtue of a perturbative approach. Stability analysis reveals that only the simplest chimeras with one synchronous region are stable.