Dynamic characterizations of foraging swarm with multi-modal Gaussian-type profiles

This paper establishes a more general continuous time swarm model with N-member. It takes the time delay and disturbances into account. We proved that the swarm members will converge and form a cohesive cluster around the center in a finite time in the presence of communication delays and disturbances. Moreover, we consider the multi-modal gaussian-type profiles, the result shows that all the swarm members will converge to more favorable areas in the presence of noise disturbances. Numerical simulations illustrate the theoretical results.