Analysis stability of multi-agents system with disturbance function

In this paper, we utilize the swarm behavior in nature for stability of the multi agents system. We propose a mathematical model describing the movement of the agent of multi agents system with disturbance function. Different from the existed models which do not disturbance. This model is a dynamics system consisting of many agents with disturbance function. The first, we study stability of the multi-agent model with disturbance function, and we do some simulation. An estimate of the time when all agents start entering the annulus is presented. The second similar behavior will also be presented in this paper that the agents aggregate and enter a certain-annulus. It is shown that the members of a swarm will aggregate and eventually form a cohesive cluster of finite size around the swarm center. In the last section will show the results of numericalsimulationof the swarm behavior with disturbance function.