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

Abstract: Phase 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.

 Fuente: Phys. Rev. E 100, 012211 (2019)

 Publisher: American Physical Society

 Publication date: 01/07/2019

 No. of pages: 14

 Publication type: Article

 DOI: 10.1103/PhysRevE.100.012211

 ISSN: 1539-3755,1550-2376,2470-0045,2470-0053

 Spanish project: FIS2016-74957-P

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