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Condensing phenomena for systems biology, ecology and sociology present in real life different complex behaviors. Based on local interaction between agents, we present another result of the Energy-based model presented by [20]. We involve an additional condition providing the total condensing (also called consensus) of a discrete positive measure. Key words: Condensing; consensus; random move; self-organizing groups; collective intelligence; stochastic modeling. AMS Subject Classifications: 81T80; 93A30; 37M05; 68U20
Local interactions between particles of a collection causes all particles to reorganize in new positions. The purpose of this paper is to construct an energy-based model of self-organizing subgroups, which describes the behavior of singular local moves of a particle. The present paper extends the Hegselmann-Krause model on consensus dynamics, where agents simultaneously move to the barycenter of all agents in an epsilon neighborhood. The Energy-based model presented here is analyzed and simulated on finite metric space. AMS Subject Classifications:81T80; 93A30; 37M05; 68U20
In this work, we extend the Hegselmann and Krause (HK) model, presented in [16] to an arbitrary metric space. We also present some theoretical analysis and some numerical results of the condensing of particles in finite and continuous metric spaces. For simulations in a finite metric space, we introduce the notion "random metric" using the split metrics studies by Dress and al. [2, 11, 12].
