Nonlinear stability of vortex formation in swarms of interacting particles.
We use a particle-based model of a swarm of interacting particles to explore analytically the conditions for the formation of vortexlike behavior. Our model uses pairwise interaction potentials to model weak long-range attraction and strong short-range repulsion with a dissipation function to align particle velocity vectors. We use the effective energy of the swarm as a Lyapunov function to prove convergence to a vortexlike state. Our analysis extends previous work which has relied purely on simulation to explore the formation and stability of vortexlike behavior through analytical rather than numerical methods.
Mabrouk
Mohamed H
MH
Department of Mechanical Engineering, University of Strathclyde, Glasgow, United Kingdom. mohamed.mabrouk@strath.ac.uk
McInnes
Colin R
CR