Time-delayed autosynchronous swarm control

Biggs, James and Bennet, Derek James and Dadzie, Kokou (2012) Time-delayed autosynchronous swarm control. Physical Review E, 85 (1). 016105. ISSN 2470-0053 (https://doi.org/10.1103/PhysRevE.85.016105)

[thumbnail of Biggs_JD_pure_Time_delayed_auto_synchronous_swarm_control_Dec_2011.pdf] PDF. Filename: Biggs_JD_pure_Time_delayed_auto_synchronous_swarm_control_Dec_2011.pdf
Preprint
Download (1MB)
[thumbnail of Biggs_JD_et_al_Pure_Time_delayed_autosynchronous_swarm_control_10_Jan_2012.pdf]
Preview
 PDF. Filename: Biggs_JD_et_al_Pure_Time_delayed_autosynchronous_swarm_control_10_Jan_2012.pdf
Final Published Version
Download (1MB)| Preview

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.

CORE (COnnecting REpositories)