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Dynamical emergent patterns of swarms are now fairly well established innature, and include flocking and rotational states. Recently, there has beengreat interest in engineering and physics to create artificial self-propelledagents that communicate over a network and operate with simple rules, with thegoal of creating emergent self-organizing swarm patterns. In this paper, weshow that when communicating networks have range dependent delays, rotationalstates which are typically periodic, undergo a bifurcation and create swarmdynamics on a torus. The observed bifurcation yields additional frequenciesinto the dynamics, which may lead to quasi-periodic behavior of the swarm.

Torus bifurcations of large-scale swarms having range dependent communication delay