Response threshold model of aggregation in a swarm: A theoretical and simulative comparison

Swarm Intelligence(SI) which is inspired by social animals has been paid more and more attention. It always appeals to the collective behaviors observed in social animals. Aiming at the feature and factors in self-organization of SI system, the aggregation behavior is studied. Firstly the response threshold model of the system is built according to the rules in aggregation. Then the stability of the steady-state solutions of the model is analyzed and the bifurcation of the steady-state solution is obtained. Finally, the effects of the parameter are analyzed based on the theory model. And the Monte Carlo simulations which give certain differences against theory results are also analyzed. All of the theoretical and simulative results show that the aggregation behavior is impacted by the relationship between the swarm size and the response threshold and sensitivity significantly. It is also proved that complex behavior emerges from local interaction of individuals. The work of this paper gives the mechanism in the emergent complex pattern of self-organized aggregation and the factors which affect the system evolution.