Abstract
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 language | English |
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Article number | 016105 |
Number of pages | 7 |
Journal | Physical Review E |
Volume | 85 |
Issue number | 1 |
Early online date | 7 Dec 2011 |
DOIs | |
Publication status | Published - 10 Jan 2012 |
Keywords
- self-propelling particles
- swarm control
- rotating swarm