| Autor: |
Hancock, Edward J., Gottwald, Georg A. |
| Rok vydání: |
2018 |
| Předmět: |
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| Zdroj: |
Phys. Rev. E 98, 012307 (2018) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1103/PhysRevE.98.012307 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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