Collective behavior of self-propelled particles with multiple delays in cross-domain scenario

In cross-domain scenarios, the simultaneous presence of multiple sensing delays exerts a profound influence on collective behavior. Motivated by this, our paper presents a system based on self-propelled particles that consists of two swarms containing two intra-swarm sensing delays and an inter-swarm sensing delay. Three state emerges from the system, namely translating state, ring state, and rotating state. Employing mean field approximation and bifurcation analysis, we theoretically examine the parameter space’s boundaries that govern these three states. Our detailed findings emphasize that within the translating and rotating states, variations in the two intra-swarm delays can lead to the separation of the two swarms. Meanwhile, the extent of separation is influenced by the inter-swarm delay. Finally, we conduct numerical simulations to validate the accuracy of our theoretical derivations.