Time-delayed autosynchronous swarm control

James Biggs, Derek James Bennet, Kokou Dadzie

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4 Citations (Scopus)
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In this paper a general Morse potential model of self-propelling particles is considered in the presence of a time-delayed term and a spring potential. It is shown that the emergent swarm behavior is dependent on the delay term and weights of the time-delayed function which can be set to induce a stationary swarm, a rotating swarm with uniform translation and a rotating swarm with a stationary center-of-mass. An analysis of the mean field equations shows that without a spring potential the motion of the center-of-mass is determined explicitly by a multi-valued function. For a non-zero spring potential the swarm converges to a vortex formation about a stationary center-of-mass, except at discrete bifurcation points where the center-of-mass will periodically trace an ellipse. The analytical results defining the behavior of the center-of-mass are shown to correspond with the numerical swarm simulations.
Original languageEnglish
Article number016105
Number of pages7
JournalPhysical Review E
Issue number1
Early online date7 Dec 2011
Publication statusPublished - 10 Jan 2012


  • self-propelling particles
  • swarm control
  • rotating swarm

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