Coordinating directional switches of multiagent systems with delayed and nonlinear interactions

Coordinating directional switches can appear in moving biological groups. Previous studies have demonstrated that the self-driven particle model can effectively describe the directional switching behaviors, but they rarely considered the effect of time delay and nonlinear interactions. Additionally, research on directional switching behavior in multiagent systems is relative few. Therefore we investigate the influence of delayed and nonlinear interactions on the directional switching movement of multiagent systems, in which response delay and transmission delay are considered. Our analysis yields the theoretical mean switching time of the movement direction, revealing that delayed and nonlinear interactions have a significant impact on the directional switches. Specifically, increasing transmission delay can suppress the directional switches when the response delay is greater than or equal to the transmission delay, and increasing transmission delay may promote the directional switching behaviors for large response delay when the response delay is less than the transmission delay. Furthermore, increasing nonlinearity in interactions may first suppress directional switching behaviors and then promote the directional switches. Our results offer valuable insights for developing bioinspired multiagent devices.