ANALYSIS OF CLUSTER AND STRIPE SOLUTIONS IN A ONE-DIMENSIONAL MODEL OF BIOLOGICAL AGGREGATION

Abstract

This thesis studies the model of swarming of organisms in groups or clusters and the solution of the interaction equation in a one dimensional biological swarm model. This process describes the behavior of some animal swarms like birds and fish that attract or repulse each other. We will discuss the formation of point clusters and conditions that relate to the number of clusters and their stability. Expanding the clusters on this analysis we will observe that the formation of stripe solutions is inevitable under certain assumption on the interaction force function. In this thesis we are interested in determining how the number of clusters and stripes depend on the functions, initial conditions and model parameters. While investigating the properties we will experiment with equal and asymmetric distributions of particles and observe that although the analytical calculations become more complicated, the same general dependence on a few simple parameters is observed.