Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 465, Issue 2103, Pages 745-768Publisher
ROYAL SOC
DOI: 10.1098/rspa.2008.0259
Keywords
multi-agent systems; self-organization; clustering; swarming; opinion formation
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Funding
- PhD fellowship of the Research Foundation Flanders (FWO)
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Clustering is a phenomenon that may emerge in multi-agent systems through self-organization: groups arise consisting of agents with similar dynamic behaviour. It is observed in fields ranging from the exact sciences to social and life sciences; consider, for example, swarm behaviour of animals or social insects, the dynamics of opinion formation or the synchronization (which corresponds to cluster formation in the phase space) of coupled oscillators modelling brain or heart cells. We consider a clustering model with a general network structure and saturating interaction functions. We derive both necessary and sufficient conditions for clustering behaviour of the model and we investigate the cluster structure for varying coupling strength. Generically, each cluster asymptotically reaches a (relative) equilibrium state. We discuss the relationship of the model to swarming, and we explain how the model equations naturally arise in a system of interconnected water basins. We also indicate how the model applies to opinion formation dynamics.
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