Filip De Smet

Clustering in a network of non-identical and mutually interacting agents

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.

Brief paper: Cluster formation in a time-varying multi-agent system

We introduce time-varying parameters in a multi-agent clustering model and we derive necessary and sufficient conditions for the occurrence of clustering behavior with respect to a given cluster structure. For periodically varying parameters the clustering conditions may be formulated in a similar way as for the time-invariant model. The results require the individual weights assigned to the agents to be constant. For time-varying weights we illustrate with an example that the obtained results can no longer be applied.

A MODEL FOR THE DYNAMICAL PROCESS OF CLUSTER FORMATION.

The formation of several clusters, arising from attracting forces between non-identical entities or agents, is a phenomenon observed in diverse fields. Think of people gathered through a mutual interest, pricing policy of different distributors in an economic market or clustering of oscillators in brain cells. We introduce a dynamical model of mutually attracting agents for which we prove that the long term behavior consists of agents organized into several groups or clusters. We have completely characterized the cluster structure by means of a set of inequalities in the parameters of the model and have identified the intensity of the attraction as a key parameter governing the transition between different cluster structures. We illustrate the relation with the Kuramoto model on interconnected oscillators and we discuss an application on compartmental systems.

Cluster transitions in a multi-agent clustering model

Clustering is a phenomenon that may emerge in multi-agent systems through self-organization: groups arise consisting of agents with similar dynamic behavior. It is observed in fields ranging from the exact sciences to social and life sciences; consider e.g. swarm behavior of animals or social insects, dynamics of opinion formation, or the synchronization (which corresponds to cluster formation in the phase space) of coupled oscillators modeling brain or heart cells.

Clustering conditions and the cluster formation process in a dynamical model of multidimensional attracting agents

We consider a multiagent clustering model where each agent belongs to a multidimensional space. We investigate its long term behavior, and we prove emergence of clustering behavior in the sense that the velocities of the agents approach asymptotic values, independently of the initial conditions; agents with equal asymptotic velocities are said to belong to the same cluster. We propose a set of relations governing these asymptotic velocities. These results are compared with results obtained earlier for the model with agents belonging to a one-dimensional space and are then explored for the case of an infinite number of agents. For the particular case of a spherically symmetric configuration of an infinite number of agents a rigorous analysis of the relations governing the asymptotic velocities is possible, assuming that a continuity property established for the finite case remains true for the infinite case. This leads to a characterization of the onset of cluster formation in terms of the evolution of the...