Model reduction for Kuramoto models with complex topologies

Abstract

Synchronisation of coupled oscillators is a ubiquitous phenomenon, occurring in topics ranging from biology and physics, to social networks and technology. A fundamental and long-time goal in the study of synchronisation has been to find low-order descriptions of complex oscillator networks and their collective dynamics. However, for the Kuramoto model - the most widely used model of coupled oscillators - this goal has remained surprisingly challenging, in particular for finite-size networks. Here, we propose a model reduction framework that effectively captures synchronisation behaviour in complex network topologies. This framework generalises a collective coordinates approach for all-to-all networks [Gottwald (2015) Chaos 25, 053111] by incorporating the graph Laplacian matrix in the collective coordinates. We first derive low dimensional evolution equations for both clustered and non-clustered oscillator networks. We then demonstrate in numerical simulations for Erdos-Renyi (ER) networks that the collective coordinates capture the synchronisation behaviour in both finite-size networks as well as in the thermodynamic limit, even in the presence of interacting clusters.

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• Synchronization in complex networks
• The Kuramoto model in complex networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Analysis of a power grid using the Kuramoto-like model
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Neuronal synchrony during anaesthesia - A thalamocortical model
• Model reduction for networks of coupled oscillators

Cited by in corpus (11)

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• Self-organized explosive synchronization in complex networks: Emergence of synchronization bombs
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• Model Reduction for the Kuramoto-Sakaguchi Model: The Importance of Non-entrained Rogue Oscillators
• Synchronization transitions in Kuramoto networks with higher-mode interaction
• Chaos in networks of coupled oscillators with multimodal natural frequency distributions
• Pattern invariance for reaction-diffusion systems on complex networks
• A collective coordinate framework to study solitary waves in stochastically perturbed Korteweg-de Vries equations
• Data-driven Selection of Coarse-Grained Models of Coupled Oscillators
• Mesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks
• Data-driven stochastic modeling of coarse-grained dynamics with finite-size effects using Langevin regression