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Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation

AuthorsLeón, Iván; Pazó, Diego CSIC ORCID
Issue Date2019
PublisherAmerican Physical Society
CitationPhysical Review E 100(1): 012211 (2019)
AbstractPhase reduction is a powerful technique that makes possible to describe the dynamics of a weakly perturbed limit-cycle oscillator in terms of its phase. For ensembles of oscillators, a classical example of phase reduction is the derivation of the Kuramoto model from the mean-field complex Ginzburg-Landau equation (MF-CGLE). Still, the Kuramoto model is a first-order phase approximation that displays either full synchronization or incoherence, but none of the nontrivial dynamics of the MF-CGLE. This fact calls for an expansion beyond the first order in the coupling constant. We develop an isochron-based scheme to obtain the second-order phase approximation, which reproduces the weak-coupling dynamics of the MF-CGLE. The practicality of our method is evidenced by extending the calculation up to third order. Each new term of the power-series expansion contributes with additional higher-order multibody (i.e., nonpairwise) interactions. This points to intricate multibody phase interactions as the source of pure collective chaos in the MF-CGLE at moderate coupling.
Publisher version (URL)https://doi.org/10.1103/PhysRevE.100.012211
Identifiersdoi: 10.1103/PhysRevE.100.012211
e-issn: 2470-0053
issn: 2470-0045
Appears in Collections:(IFCA) Artículos
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