Seminar 21.11.2019: Jan Haskovec

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 21.11.2019: Jan Haskovec

Postby quittner » Mon Nov 11, 2019 3:50 pm

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Thursday 21.11.2019 at 14:00 Lecture room M-223

Jan Haškovec (KAUST):
Asymptotics of alignment and consensus models with delays

We study the impact of communication or reaction delays on the long-time behavior
of alignment/consensus models of Cucker-Smale type. For a model where agents
interact with each other through normalized communication weights,
we provide sufficient conditions for asymptotic flocking, i.e., convergence to a
common velocity vector, based on a construction of a suitable Lyapunov functional.
For a model without normalization, we present new stability estimates
for the particle flow, relating suitable delayed and non-delayed quantities.
We also briefly explain how multiplicative noise affects the long-time
dynamics and present results of systematic numerical simulations.
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