Collective motion patterns of swarms with delay coupling: theory and experiment

Abstract

The formation of coherent patterns in swarms of interacting self-propelled autonomous agents is a subject of great interest in a wide range of application areas, ranging from engineering and physics to biology. In this paper, we model and experimentally realize a mixed-reality large-scale swarm of delay-coupled agents. The coupling term is modeled as a delayed communication relay of position. Our analyses, assuming agents communicating over an Erdos-Renyi network, demonstrate the existence of stable coherent patterns that can only be achieved with delay coupling and that are robust to decreasing network connectivity and heterogeneity in agent dynamics. We also show how the bifurcation structure for emergence of different patterns changes with heterogeneity in agent acceleration capabilities and limited connectivity in the network as a function of coupling strength and delay. Our results are verified through simulation as well as preliminary experimental results of delay-induced pattern formation in a mixed-reality swarm.

arXiv comment11 pages, 11 Figures. arXiv admin note: text overlap with arXiv:1507.03586

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• Critical transition for colliding swarms
• Stability of milling patterns in self-propelled swarms on surfaces
• Torus bifurcations of large-scale swarms having range dependent communication delay
• The impact of catastrophic collisions and collision avoidance on a swarming behavior
• The Dynamics of Interacting Swarms
• Asymptotic behavior of the linear consensus model with delay and anticipation
• Asymmetric noise-induced large fluctuations in coupled systems