@article{10902/18526,
year = {2019},
month = {7},
url = {http://hdl.handle.net/10902/18526},
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.},
organization = {We acknowledge support by MINECO (Spain) under Project No. FIS2016-74957-P. IL acknowledges support by Universidad de Cantabria and Government of Cantabria under the Concepción Arenal programme.},
publisher = {American Physical Society},
publisher = {Phys. Rev. E 100, 012211 (2019)},
title = {Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation},
author = {León Merino, Iván and Pazó Bueno, Diego Santiago},
}