2019/07/19 by Iván León, Diego Pazó · 4 citations
Computer Science · Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Coupling (piping) #Ecosystem dynamics and resilience #Field (mathematics) #Geometry #Kuramoto model #Limit (mathematics) #Limit cycle #Mathematical analysis #Mathematics #Mean field theory #Nonlinear Dynamics and Pattern Formation #Phase (matter) #Physics #Quantum mechanics #Reduction (mathematics) #Slime Mold and Myxomycetes Research #Statistical physics #Synchronization (alternating current) #Topology (electrical circuits) #nlin.AO #nlin.CD
paper · pdf · doi:10.1103/physreve.100.012211
published as Phys. Rev. E 100, 012211 (2019) · 15 pages
openalex publication_date 2019/07/19 · arxiv created 2019/07/22 · arxiv updated 2019/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.