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

Abstract:

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.