Chimera States for Coupled Oscillators

Daniel M. Abrams and Steven H. Strogatz
Phys. Rev. Lett. 93, 174102 – Published 22 October 2004

Abstract

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 spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera state.

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  • Received 19 July 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.174102

©2004 American Physical Society

Authors & Affiliations

Daniel M. Abrams* and Steven H. Strogatz

  • Department of Theoretical and Applied Mechanics, Cornell University, 212 Kimball Hall, Ithaca, New York 14853-1503, USA

  • *Electronic address: dma32@cornell.edu
  • Electronic address: shs7@cornell.edu

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Issue

Vol. 93, Iss. 17 — 22 October 2004

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