# Chimera states for coupled oscillators.

@article{Abrams2004ChimeraSF, title={Chimera states for coupled oscillators.}, author={Daniel M. Abrams and Steven H. Strogatz}, journal={Physical review letters}, year={2004}, volume={93 17}, pages={ 174102 } }

Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a… Expand

#### 834 Citations

Solvable model for chimera states of coupled oscillators.

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The first exact results about the stability, dynamics, and bifurcations of chimera states are obtained by analyzing a minimal model consisting of two interacting populations of oscillators. Expand

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It is demonstrated for the first time the existence of a chimera state with only two diffusively coupled identical oscillators, one behaving nearly periodically ( coherently) and the other chaotically (incoherently). Expand

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This work reports the coexistence of coherent and incoherent domains, called chimera states, in an array of identical Duffing oscillators coupled to their nearest neighbors, characterized by their Lyapunov spectra and their global phase coherence order parameter. Expand

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Defining a "weak chimera" as a type of invariant set showing partial frequency synchronization, it is shown that they cannot appear in phase oscillator networks that are either globally coupled or too small. Expand

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A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist. This state of broken symmetry, which usually… Expand

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It is shown that the smallest chimera state, characterized by the coexistence of two synchronized and one incoherent oscillator, can be observed in simple experiments with mechanical oscillators, which are controlled by elementary dynamical equations derived from Newton’s laws. Expand

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A prototype model of chimera states corresponding to the coexistence of incoherent domains is revealed and these freak states emerge through a bifurcation in which the coherent domain of an existing chimera state experiences an instability giving rise to another incoherent state. Expand

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Heterogeneous models for which the natural frequencies of the oscillators are chosen from a distribution are studied, finding that heterogeneity can destroy chimerae, destroy all states except chimerAE, or destabilize Chimerae in Hopf bifurcations, depending on the form of the heterogeneity. Expand

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Chimera states in a system with linear local connections have been studied. The system is a ring ensemble of analog bistable self-excited oscillators with a resistive coupling. It has been shown that… Expand

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Novel clustered chimera states are found that have spatially distributed phase coherence separated by incoherence with adjacent coherent regions in antiphase through time-delay induced phase clustering. Expand

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