Chimera states for coupled oscillators.

By Daniel M. Abrams, Steven H. Strogatz. Physical Review Letters, 2004

1,186 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/5a77d104c42205fbaff73005c0d953af344a361a

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Citations in the corpus

The dynamics of chimera states in heterogeneous Kuramoto networks (2009, background): “We find that z satisfies ∂z ∂t = (iΩ −D)z + (i/2) [ R̂e + R̂ez(2) ] (13) where R̂(x, t) = ∫ π −π G(x− y)z(y, t) dy (14) As other authors have done [7,10,12] we assume thatG(x) = (1+A cosx)/(2π), and that z is even in x.”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “[364] Daniel M Abrams and Steven H Strogatz.”
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)”
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization (2016, background): “In the previous Sections, a variety of coherent states emerging in the classical Kuramoto model have been discussed and characterized, such as the partially coherent state [237], the standing-wave [243, 335] and TW [243, 394] states, and the chimera state [217, 219, 395, 396].”
Spontaneous synchrony in power-grid networks (2013, methodology): “systems have non-identical βi values (Table 1, column 7), their stability was determined directly from equations (4) and (5) before diagonalization; the stability is quantified by λ, the largest Lyapunov exponent excluding the null exponent associated with the uniform shift of phases.”
Coherence–incoherence patterns in a ring of non-locally coupled phase oscillators (2013, background): “It is a surprising fact that almost all previous studies related to the topic reported only on the secondary coherence-incoherence pattern corresponding to the first Fourier coefficient g1, see for example [12, 14, 15, 19, 20].”
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].”
Sensitivity and Nonlinearity of Thermoacoustic Oscillations (2018, background): “They also showed that, during intermittency, patches of synchronous and asynchronous motion coexist in the reaction zone, which is known as a chimera state (Abrams & Strogatz 2004).”
Experimental observation of chimeras in coupled-map lattices (2012, methodology): “Taking into account the local dynamics, we define the following function as a deviation from equation (3)”
Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings (2014, background): “We remark that this observation suggests a new and alternative way of measuring generalized synchronization or synchronization among a partial set of nodes in a large-scale network [27,28].”