  Swarm and modular robotics are an emerging area in control of autonomous
systems. However, coordinating a large group of interacting autonomous agents
requires careful consideration of the logistical issues involved. In
particular, inter-agent communication generally involves time delay, and
bandwidth restrictions limit the number of neighbors with which each agent in
the swarm can communicate. In this paper, we analyze coherent pattern dynamics
of groups of delay-coupled agents, where the communication network is an
Erdos-Renyi graph. We show that overall motion patterns for a globally-coupled
swarm persist under decreasing network connectivity, and derive the bifurcation
structure scaling re- lations for the emergence of different swarming behaviors
as a function of the average network degree. We show excellent agreement
between the theoretical scaling results and numerical simulations.
