A class of attraction/repulsion functions for stable swarm aggregations

In this article, for an M-member "individual-based" continuous time swarm model in an n-dimensional space, we extend our previous results (2002) by specifying a general class of attraction/repulsion functions that can be used to achieve swarm aggregation. These functions are odd functions that have terms for attraction and repulsion acting in opposite directions in compliance with real biological swarms. We present a stability analysis for several cases of the functions considered to characterize the swarm cohesiveness, size, and ultimate motions while in a cohesive group.