Transient cluster formation in generalized Hegselmann-Krause opinion dynamics

We analyse the generalized Hegselmann-Krause model of opinion dynamics. The asymptotic state of such a system has been well studied in the literature, however the transient state is still poorly understood. Predicting which groups of agents will form clusters remains to be studied. We present sufficient conditions to detect cluster formation in the transient phase of the multi-agent system. We also give a procedure to know how much time a cluster stays consistent, i.e., before it merges with other agents in the system. Our criterion can be computed locally using variables obtained from the initial conditions. Finally our results are illustrated by a numerical example.

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