WIAS Preprint No. 2450, (2017)

The mathematics behind chimera states



Authors

  • Omel'chenko, Oleh E.
    ORCID: 0000-0003-0526-1878

2010 Mathematics Subject Classification

  • 34C15 35B36 35B32 35Q83 35Q84 34H10

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt 89.75.Kd

Keywords

  • Coupled oscillators, pattern formation, spatial chaos, chimera states, coherence-incoherence patterns

DOI

10.20347/WIAS.PREPRINT.2450

Abstract

Chimera states are self-organized spatiotemporal patterns of coexisting coherence and incoherence. We give an overview of the main mathematical methods used in studies of chimera states, focusing on chimera states in spatially extended coupled oscillator systems. We discuss the continuum limit approach to these states, Ott--Antonsen manifold reduction, finite size chimera states, control of chimera states and the influence of system design on the type of chimera state that is observed.

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