Work

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

Year: 2019

Type: article

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.

Source: Physical review. E

DOI: 10.1103/physreve.100.012211

Authors: Iván León, Diego Pazó

Institutions: Universidad de Cantabria, Instituto de Física de Cantabria

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Universidad de Cantabria, Ministerio de Asuntos Económicos y Transformación Digital, Gobierno de España

Award: G2190616802