# Impacts of time delay on flocking dynamics of a two-agent flock model

Published on May 1, 2019in Communications in Nonlinear Science and Numerical Simulation4.26

· DOI :10.1016/J.CNSNS.2018.10.017

Abstract

Abstract Due to finite information transmission and processing time between agents, delays are inevitable and should therefore be incorporated into flocking modeling. To shed light on understanding the impacts of time delay on the dynamics of flock models, we incorporate a time delay to a two-agent flock model and study its flocking dynamics. When the product of the amplitude of the coupling strength and the time delay is relatively small, necessary and sufficient conditions are established for the two-agent flock model to exhibit flocking. We further show that as the delay increases, transcritical bifurcation and Hopf bifurcation may emerge resulting in rich and complex flocking dynamics.