Mesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks
Autor: | Georg A. Gottwald, Lauren D. Smith |
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Rok vydání: | 2021 |
Předmět: |
Collective behavior
Mesoscopic physics Computational complexity theory Computer science Applied Mathematics FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics 01 natural sciences Nonlinear Sciences - Adaptation and Self-Organizing Systems 010305 fluids & plasmas Reduction (complexity) 0103 physical sciences Synchronization (computer science) Thermodynamic limit Node (circuits) Statistical physics 010306 general physics Adaptation and Self-Organizing Systems (nlin.AO) Mathematical Physics Bifurcation |
Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science. 31:073116 |
ISSN: | 1089-7682 1054-1500 |
DOI: | 10.1063/5.0053916 |
Popis: | The behavior at bifurcation from global synchronization to partial synchronization in finite networks of coupled oscillators is a complex phenomenon, involving the intricate dynamics of one or more oscillators with the remaining synchronized oscillators. This is not captured well by standard macroscopic model reduction techniques which capture only the collective behavior of synchronized oscillators in the thermodynamic limit. We introduce two mesoscopic model reductions for finite sparse networks of coupled oscillators to quantitatively capture the dynamics close to bifurcation from global to partial synchronization. Our model reduction builds upon the method of collective coordinates. We first show that standard collective coordinate reduction has difficulties capturing this bifurcation. We identify a particular topological structure at bifurcation consisting of a main synchronized cluster, the oscillator that desynchronizes at bifurcation, and an intermediary node connecting them. Utilizing this structure and ensemble averages we derive an analytic expression for the mismatch between the true bifurcation from global to partial synchronization and its estimate calculated via the collective coordinate approach. This allows to calibrate the standard collective coordinate approach without prior knowledge of which node will desynchronize. We introduce a second mesoscopic reduction, utilizing the same particular topological structure, which allows for a quantitative dynamical description of the phases near bifurcation. The mesoscopic reductions significantly reduce the computational complexity of the collective coordinate approach, reducing from $\mathcal{O}(N^2)$ to $\mathcal{O}(1)$. We perform numerical simulations for Erd\H{o}s-R\'enyi networks and for modified Barab\'asi-Albert networks demonstrating excellent quantitative agreement at and close to bifurcation. |
Databáze: | OpenAIRE |
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