Continuous-time average-preserving opinion dynamics with opinion-dependent communications

We study a simple continuous-time multi-agent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an intensity proportional to the difference. We prove convergence to a set of clusters, with the agents in each cluster sharing a common value, and provide a lower bound on the distance between clusters at a stable equilibrium, under a suitable notion of multi-agent system stability. To better understand the behavior of the system for a large number of agents, we introduce a variant involving a continuum of agents. We prove, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a non-trivial lower bound on the distance between clusters. Finally, we establish that the continuum model accurately represents the asymptotic behavior of a system with a finite but large number of agents.Comment: 25 pages, 2 figures, 11 tex files and 2 eps file

Een modelonderzoek naar het mechanisme van de natuurlijke verdichting van een zandgrond

In het kader van het onderzoek aan bodemverdichting na een losmakende bewerking door de afdeling bodemtechniek, wil men nagaan welke de mechanismen van natuurlijke bodemverdichting zijn