The mathematics behind chimera states

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 appro...

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Bibliographic Details
Published inNonlinearity Vol. 31; no. 5; pp. R121 - R164
Main Author Omel'chenko, O E
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.05.2018
Subjects
chimera states
coherence-incoherence patterns
continuum limit equation
control theory
coupled oscillators
finite size effects
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Summary: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.
Bibliography:NON-102166.R2
London Mathematical Society
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aaaa07