Dynamics of Swarms and Opinions via Discrete Positive Systems

Tuesday, October 27, 2015 - 4:00pm to Wednesday, October 28, 2015 - 3:55pm

Event Calendar Category

LIDS Seminar Series

Speaker Name

Ulrich Krause


Universit├Ąt Bremen

Building and Room Number



In the talk a general model for swarm formation of birds (or other agents) will be presented. Swarm formation means that birds approach asymptotically the same velocity, whereby distances among them do converge. The main result offers conditions on the local interaction of the birds for swarm formation to happen. Roughly speaking, the structure of interaction should not be "too loose" and the intensity of interaction should not decay "too fast". Furthermore, the various flight regimes, for example echelons, occurring in swarm formation, will be analyzed. What if the interaction of birds (or other agents) is too loose and/or decays too fast? In this case, a further result will describe how an ensemble of birds splits into sub-swarms. The same result also applies to opinion dynamics and the formation of a consensus or of a fragmentation among the opinions of a group of agents. For analyzing the convergence behavior, the field of positive dynamical systems in discrete time provides useful tools when dealing with infinite products of matrices or with the iteration of averaging maps.


Ulrich Krause is professor emeritus at the Department of Mathematics, University of Bremen, Bremen, Germany. He holds a PhD. in mathematics and a PhD. in economics. His main field of interest is positive dynamical systems, including applications to biology and economics. He has written many books on mathematics and on economics, as well as numerous articles within these fields, including articles on algebraic number theory, opinion dynamics, decision theory, social choice. His most recent book is Positive dynamical systems in discrete time. Theory, models, and applications, De Gruyter, Berlin, 2015.