Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators

By Y. Kuramoto, D. Battogtokh. 2002

737 citations recorded by the source corpus.

The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into two domains, one composed of mutually synchronized oscillators with unique frequency and the other composed of desynchronized oscillators with distributed frequencies. We apply a theory similar to the one which successfully explained the onset of collective synchronization in globally coupled phase oscillators with frequency distribution. A space-dependent order parameter is thus introduced, and an exact functional self-consistency equation is derived for this quantity. Its numerical solution is confirmed to reproduce the simulation results accurately.

Subfields: Atomic and Molecular Physics, and Optics, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f49692d808c31b445157377ecb70a5eb77b574df

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In Atomic and Molecular Physics, and Optics

In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Hidden attractors in dynamical systems (2016, background): “[182] Y. Kuramoto, D. Battogtokh, Coexistence of coherence and incoherence in nonlocally coupled phase oscillators, Nonl.”
Coherence–incoherence patterns in a ring of non-locally coupled phase oscillators (2013, methodology): “Such coherenceincoherence patterns attracted great interest and have been the subject of numerous studies in last decade [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30].”
The Metastable Brain (2014, positive): “An example of such coordination dynamics with components obeying Equation 2 (after Kuramoto and Battogtokh, 2002) is presented in Figure 2A, d dt fðx; tÞ=u Z p p G x x0 sin fðx; tÞ f x0 ; t +a dx0 ; (Equation 2) where f is the time (t) and space (x)-dependent phase of oscillators x arranged in a…”
Experimental observation of chimeras in coupled-map lattices (2012, methodology): “k,l=−R [ I ( φ i+k,j+l ) − I ( φ i,j )]} (2)”
The dynamics of chimera states in heterogeneous Kuramoto networks (2009, methodology): “First rewrite (27) as dφ i dt = ω i + K i sin β + K i N N j=1 sin(φ j − φ i − β) (29) In the continuum limit, we again assume the existence of a probability density function f (K, ω, φ, t) which satisfies the continuity equation ∂f ∂t + ∂ ∂φ (f v) = 0 (30) where v = ω + K sin β + K ∞ 0 Γ(K) ∞ −∞ 2π ”
Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators (2014, background): “Kd, 05.65.+b Mathematics Subject Classification: 34C15, 34C23, 35B36, 82C22, 82C44 (Some figures may appear in colour only in the online journal)”
Phase reduction approach to synchronisation of nonlinear oscillators (2016, background): “In particular, the “chimera states” in nonlocally coupled phase models have been intensively studied [83, 84].”