CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS
Author(s)Blondel, Vincent D.; Hendrickx, Julien; Tsitsiklis, John N.
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We study a simple continuous-time multiagent 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 multiagent 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 nontrivial 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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
SIAM Journal on Control and Optimization
Society for Industrial and Applied Mathematics
Blondel, Vincent D., Julien M. Hendrickx, and John N. Tsitsiklis. “Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications.” SIAM Journal on Control and Optimization 48.8 (2010) : 5214. © 2010 Society for Industrial and Applied Mathematics
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