Stability analysis of social foraging swarms: combined effects of attractant/repellent profiles

In this paper we study the stability of the collective behavior of social foraging swarms, i.e., swarms moving in a profile of nutrient/toxic substances (an attractant/repellent profile) and extend our previous results. In particular, we consider a plane profile and also extend our results for the quadratic, Gaussian, and multi-modal Gaussian profiles. Moreover, we analyze the ultimate behavior of the individuals in the social foraging swarm. The paper closes with new simulation studies that give insights into swarm dynamics.