Swarming, or aggregations of organisms in groups, can be found in nature in many organisms ranging from simple bacteria to mammals. Such behavior can result from several different mechanisms. For example, individuals may respond directly to local physical cues such as concentration of nutrients or distribution of some chemicals as seen in some bacteria and social insects, or they may respond directly to other individuals as seen in fish, birds, and herds of mammals. In this dissertation, we

Abstract-In this article we specify an -member "individual-based" continuous time swarm model with individuals that move in an -dimensional space according to an attractant/repellent or a nutrient profile. The motion of each individual is determined by three factors: 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 (or repulsion from the unfavorable regions) of the attractant/repellent profile. The emergent behavior of the swarm motion is the result of a balance between inter-individual interactions and the simultaneous interactions of the swarm members with their environment. 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.

Swarming, or aggregations of organisms in groups, can be found in nature in many organisms ranging from simple bacteria to mammals. Such behavior can result from several different mechanisms. For example, individuals may respond directly to local physical cues such as concentration of nutrients or distribution of some chemicals as seen in some bacteria and social insects, or they may respond directly to other individuals as seen in fish, birds, and herds of mammals. In this dissertation, we

In this brief article, we consider an M-member 'individual-based' continuous time swarm model in an n-dimensional space and extend the results in Gazi and Passino (2003) 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 stability analysis for several cases of the functions considered to characterize swarm cohesiveness, size and ultimate motions while in a cohesive group. Moreover, we show how the model can be extended for achieving formation control. Furthermore, we discuss how the attraction repulsion functions can be modified to incorporate the finite body size of the swarm members. Numerical simulations are also presented for illustration purposes.