Stability analysis of a class of social foraging swarms with general nonlinear structure

In this paper we consider a class of social foraging swarms with nutrient/toxic profiles and general nonlinear attraction and repulsion structure. The emergent behavior of the swarm motion is the result of a balance between inter-individuals interactions and the simultaneous interactions of the swarm with their environment. The interactions among the swarm members considered in the paper is varying in different situations. The paper considers a condition under which the agents of the reciprocal swarm will aggregate and eventually form a cohesive cluster of finite size for different profiles under some very mild assumptions. We present several numerical simulations to show the theoretical results is correct. For general non-reciprocal swarms, numerical simulations show that more complex oscillation may occur in the behavior of swarms.