Emergent motion patterns of delay-coupled swarms

Emergent pattern-forming behaviours of aggregates of interacting autonomous agents are a topic of great interest in complex systems research, with applications including biology, environmental monitoring, and defence. We model, and experimentally verify, pattern formation in a swarm of delay-coupled agents, using a simple but general model of agent interactions. Using mean-field dynamics, we perform a thorough analytical study of the bifurcation structure as a function of network connectivity and delay to describe the emergence of pattern formation. We show that swarm motion patterns observed for a homogeneous swarm with all-to-all communication are robust to decreasing network connectivity and to heterogeneity in the parameters governing individual agent behaviours. We perform systematic numerical studies to show where the mean-field theory deviates from simulation and experiment.