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The dynamics of chimera states in heterogeneous Kuramoto networks. (English) Zbl 1185.34042
The paper presents a number of analytical results concerning emergence and stability of chimera states in networks of coupled phase oscillators. The chimera states have previously been discovered as a surprise in networks of symmetrically coupled identical oscillators, where the population spontaneously splits into synchronized and desynchronized subpopulations. The present paper reports on the existence and stability of the chimera states for nonidentical oscillators if a heterogeneity of the natural frequencies is introduced. It is shown that a power-law ansatz for the probability density function recently discovered by Ott and Antonsen provides an effective tool for the investigation of stationary states of the evolutionary equation of the network. The paper addresses a variety of models including one- and two-dimensional oscillator arrays with non-local coupling, all-to-all coupled networks with inhomogeneous coupling strengths as well as delay-coupled oscillator ensembles. Bifurcation analysis of the stationary chimera states demonstrates that these states are robust with respect to small heterogeneity in the networks. The obtained analytical results are illustrated by numerical simulations.

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations
AUTO; HomCont
Full Text: DOI
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