Abstract
We propose a simple swarm model to study collective behaviour of a group of mobile autonomous agents interacting through a long range attraction and short range repulsion function. It is shown that the individuals (agents) will aggregate and eventually form a cohesive cluster of finite size around the swarm centre in a finite time, and the size depends only on the parameters of the swarm model. Furthermore, it is also shown that all the individuals will converge to equilibrium positions of the swarm model, and thus the configuration of the swarm converges to a constant constellation. Numerical simulations are also worked out to illustrate the analytical results.