Stability analysis of local swarms in an environment with a quadratic profile

This paper first constructs an model of local swarms with a quadratic profile. Then study the stability properties of the collective behavior of the swarm and provide conditions for collective convergence to more favorable regions of the profile. It is shown that the individuals of the swarms will aggregate and eventually enter into a bounded hyperball around the swarm center or objective position. Aimed at removing the local trap, this paper gives the bound of parameter A_δ.