Delay-induced directional switches and mean switching time in swarming systems

Abstract

Coordinated directional switches often emerge in moving biological groups replete with individual-level interactions. Recent self-propelled particles models can somewhat mimic the patterns of directional switches, but they usually do not include the effects of time delays in the interactions. Here, we focus on investigating the influence of time-delay interactions on the collective motion of swarming locusts, an experimentally well-studied system that exhibits ordered switches between clockwise and counterclockwise movement. We show, both analytically and numerically, that time delays of different types can affect the directional switches. Specifically, for the sufficiently small response delay, increasing the transmission delay can increase the mean switching time, while, for the large response delay, increasing the transmission delay may destroy the ordered directional switches. Our results decipher the role of time-delay interactions in the collective motion, which could be beneficial to the design of collective intelligent devices.