- Condensing on metric spaces : modeling, analysis and simulation (2009)
- In this work, we extend the Hegselmann and Krause (HK) model, presented in  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].
- Energy-based model of forming subgroups on finite metric space (2009)
- 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
- Condensing of self-organizing groups (2010)
- 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 . 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