On Krause's consensus formation model with state-dependent connectivity
Vincent Blondel, Université catholique de LouvainPresentation Blondel
Abstract. We study a model of opinion dynamics introduced by Krause: each agent has an opinion represented by a real number, and updates its opinion by averaging all agent opinions that differ from its own by less than 1. We give a simple proof of convergence into clusters of agents, with all agents in the same cluster holding the same opinion. We then introduce a particular notion of equilibrium stability and provide lower bounds on the inter-cluster distances at a stable equilibrium. To better understand the behavior of the system when the number of agents is large, we also introduce and study a variant involving a continuum of agents, obtaining partial convergence results and lower bounds on inter-cluster distances, under some mild assumptions.Joint work with Julien M. Hendrickx and John N. Tsitsiklis.
Biography. Vincent D. Blondel is professor and head of the department of mathematical engineering at the Université catholique de Louvain (UCL) in Belgium. He received an engineering degree, a degree in philosophy, and a PhD in applied mathematics, all from the Université catholique de Louvain, and a MSc in pure mathematics from Imperial College (London, UK). He has also completed a master thesis at the Institut National Polytechnique de Grenoble (France). He was a visiting scientist at Oxford University in 1993. During the academic year 1993-1994, he was the Göran Gustafsson Fellow at the Royal Institute of Technology (Stockholm, Sweden). In 1993-1994 he was a research fellow a the French national research center in computer science (INRIA, Rocquencourt, Paris). From 1994 to 1999 he was an associate professor at the Institute of Mathematics of the Université de Liège in Belgium. Dr Blondel was a visitor with the Australian National University (1991), the University of California at Berkeley (1998), the Santa Fe Institute (2000) and Harvard University (2001). He has also been an invited professor at the Ecole Normale Supérieure in Lyon (1998) and at the University of Paris VII (1999 and 2000). In 2005-2006 he was an invited professor and Fulbright scholar with the Department of Electrical Engineering and Computer Sciences of the Massachusetts Institute of Technology (Cambridge, USA).
Dr Blondel's major current research interests lie in several area of mathematical control theory and theoretical computer science. He is a former associate editor of the European Journal of Control (Springer) and an associate editor of Systems and Control Letters (Elsevier) and of the Journal on Mathematics of Control, Signals, and Systems (Springer). For his scientific contributions he has been awarded of a grant from the Trustees of the Mathematics Institute of Oxford University (1992), the prize Agathon De Potter of the Belgian Royal Academy of Science (1993), the prize Paul Dubois of the Montefiore Institute (1993), the triennal SIAM prize on control and systems theory (2001), the prize Adolphe Wetrems of the Belgian Royal Academy of Science (2006), and the Antonio Ruberti prize in systems and control of the IEEE (2006).