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Stability analysis of swarms in an environment with an attractant/repellent profile

In this article we specify an "individual-based" continuous time swarm model in n-dimensional space with an attractant/repellent profile. The motion of each individual is determined by three components: (i) attraction to the other individuals on long distances, (ii) repulsion from the other individuals on short distances, and (iii) attraction to the more favorable regions of the attractant/repellent profile. We study the stability properties of the collective behavior of the swarm for different profiles and provide conditions for collective convergence to more favorable regions of the profile.