Swarm and modular robotics are an emerging area in control of autonomoussystems. However, coordinating a large group of interacting autonomous agentsrequires careful consideration of the logistical issues involved. Inparticular, inter-agent communication generally involves time delay, andbandwidth restrictions limit the number of neighbors with which each agent inthe swarm can communicate. In this paper, we analyze coherent pattern dynamicsof groups of delay-coupled agents, where the communication network is anErdos-Renyi graph. We show that overall motion patterns for a globally-coupledswarm persist under decreasing network connectivity, and derive the bifurcationstructure scaling re- lations for the emergence of different swarming behaviorsas a function of the average network degree. We show excellent agreementbetween the theoretical scaling results and numerical simulations.
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