Flocking estimates of the linear consensus models with a time-delay

Abstract

In this thesis, we present the flocking dynamics for linear consensus models with a time-delay. Our linear consensus models include the special case of the Cucker-Smale flocking model with constant communication rates. For some linear consensus models, we provide explicit asymptotic value for velocity in terms of the initial data and constant time-delay and exponential convergence of velocity dynamics toward the asymptotic value. We also present several numerical simulations and compare them with analytical results.