Collective Dynamics of Swarms with a New Attraction/Repulsion Function

We specify an “individual-based” continuous-time model for swarm aggregation in -dimensional Euclidean space. We show that the swarm is completely stable, and the center of the swarm is stationary. Numerical simulations indicate that the individuals will form a stable and cohesive swarm, and under the attraction/repulsion function, the bound of the swarm size will increase as the number of individuals increases