Stability analysis of swarming model with time delays

Abstract

A swarming model is a model that describes the behavior of the social aggregation of a large group of animals or the community of humans. In this work, the swarming model that includes the short-range repulsion and long-range attraction with the presence of time delay is investigated. Moreover, the convergence to a consensus representing dispersion and cohesion properties is proved by using the Lyapunov functional approach. Finally, numerical results are provided to demonstrate the effect of time delay on the motion of the group of agents.