Abstract

Collective animal behaviour is often modelled by individual-based models which assume that each individual alters its behaviour according to signals in its neighborhoods. Basic self-propelled particle models can successfully explain some experimentally observed group-level properties, but additional conjectures have to be hypothesized at the individual-level to fully explain experimental data .  In this talk, we will discuss the influence of time delay and noise on the collective  behavior of self-propelled particles system. Firstly, we consider the directional switching of a self-driven particle model with constant, time-varying and random delay times, respectively. The presented analytical and numerical results have demonstrated that time delay can facilitate coherence in self-driven interacting particle systems. Then we discuss the effect of noise on the convergence speed of a stochastic  Cucker-Smale system. We show that noise can accelerate the emergence of flocking.