Solvable model for chimera states of coupled oscillators

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Abrams, Daniel M.
Mirollo, Renato E.
Strogatz, Steven H.
Wiley, Daniel A.
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Abstract
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Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized sub-populations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf and homoclinic bifurcations of chimeras.
Comment: 4 pages, 4 figures. This version corrects a previous error in Figure 3, where the sign of the phase angle psi was inconsistent with Equation 12
Keywords
Nonlinear Sciences - Chaotic Dynamics, Mathematics - Dynamical Systems, Nonlinear Sciences - Pattern Formation and Solitons
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