Swarms and Opinions by Positive Dynamical Systems

How are birds able to coordinate themselves in swarms? It seems as if they arrive at
some consensus regarding their velocities. Indeed, swarm formation can be understood
by analysing how consensus is approached in models of opinion dynamics.
On this understanding the talk presents a general model of swarm dynamics which will
be related also to the famous, albeit more special, Cucker-Smale model of
flocking. The alignment of birds in swarms (or of other "agents", too) occurs by averaging over velocities of neighbors wherefore the interaction is modeled by positive matrices which vary with time. For this reason the analysis uses tools from the field of positive dynamical systems
as it will be explained in the talk.



References


[1]F. Cucker, S. Smale, Emergent Behavior in Flocks, IEEE Transactions on Automatic
Control 52(5)(2007), 852-862.

[2] R. Hegselmann, U. Krause, Opinion Dynamics and Bounded Confidence - Models,
Analysis, and Simulation, Journal of Artifical Societies and Social Simulation (JASSS)
5(3) (2002), http://jasss.soc.surrey.ac.uk/5/3/2.html.

[3] U. Krause, Positive Dynamical Systems in Discrete Time. Theory, Models, and Applications, De Gruyter, Berlin (2015).