Globally Asymptotically Stable for Exponential Type Stochastic Swarms

A novel Lagrangian ¿individual-based¿ isotropic continuous time exponential type stochastic swarming model in an n-dimensional Euclidean space with a family of attraction/repulsion function is proposed in this article. The stability of aggregating behavior of the swarms system are verified by stability theoretical analysis and numerical simulation. Stability analysis and numerical simulations results further indicate that the individual members living in group during the course of coordinative motion can realize the mutual aggregating behavior, the motion of each individual member is a combination of the inter-individual interactions, meanwhile, which are also presented to demonstrate the effectiveness of our model. The attraction/repulsion function is odd, so the attractive force and repulsion force taking effect in opposite direction that leads to aggregation behavior. Moreover, numerical simulation results of globally asymptotically stability analysis also verify the capability of the proposed relevant theories.