2005/02/09 by Sung Joon Moon, Ioannis G. Kevrekidis
Computer Science · Engineering · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research #Theoretical and Computational Physics #nlin.AO #nlin.PS
paper · pdf · doi:10.1142/s021812740601588x
published as Int. J. Bifurcation and Chaos, 16(7) 2043-2052 (2006) · submitted to the {\it International Journal of Bifurcations and Chaos}
arxiv created 2005/02/09 · openalex publication_date 2006/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an equation-free multiscale approach to the computational study of the collective dynamics of the Kuramoto model [Kuramoto, 1984], a prototypical model for coupled oscillator populations. Our study takes place in a reduced phase space of coarse-grained "observables" of the system: the first few moments of the oscillator phase angle distribution. We circumvent the derivation of explicit dynamical equations (approximately) governing the evolution of these coarse-grained macroscopic variables; instead we use the equation-free framework [Kevrekidis et al., 2003] to computationally solve these equations without obtaining them in closed form. In this approach, the numerical tasks for the conceptually existing but unavailable coarse-grained equations are implemented through short bursts of appropriately initialized simulations of the "fine-scale", detailed coupled oscillator model. Coarse projective integration and coarse fixed point computations are illustrated.