Consensus formation models with delay

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Jan Haskovec, AMCS, KAUST


 Individual-based models of collective behavior represent a very active research field with applications in physics (spontaneous magnetization), biology (flocking and swarming) and social sciences (opinion formation). They are also a hot topic engineering (swarm robotics).  A particularly interesting aspect of the dynamics of multi-agent systems is the emergence of global self-organized patterns, while individuals typically interact only on short scales. In this talk I shall discuss the impact of delay on asymptotic consensus formation in Hegselmann-Krause-type models, where agents adapt their „opinions“ (in broad sense) to the ones of their close neighbors. We shall understand the two principial types/sources of delay - information propagation and processing - and explain their qualitatively different impacts on the consensus dynamics. We then discuss various mathematical methods that provide asymptotic consensus results in the respective settings: Lyapunov functional-type approach, direct estimates, convexity arguments and forward-backward estimates.

Brief Biography

1999-2003 MSc. in Applied Mathematics, Charles U. in Prague

2003-2008 PhD. in Applied Mathematics, U. of Vienna

2008-2009 Postdoc in PDE Analysis, Vienna U. of Technology

2009-2012 Postdoc in PDE Analysis, Johann Radon Institute, Linz

2012-present Research Scientist, CEMSE, KAUST

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