Chemotaxis Models for Biological Pattern Formation: A case study of Forager-Scrounger-Prey Systems

Abstract

This thesis investigates the use of mathematical models to understand pattern formation processes in biology that arise due to self-organisation, in particular, chemotaxis. Chemotaxis models are one of the principal mathematical models used to describe biological pattern formation. This thesis aims to study biological self-organisation via the chemotaxis model and demonstrate how far the chemotaxis model helps understand these events. The thesis will start by deriving the chemotaxis model using two different methods, which are a mass conservation argument and a biased space-jump random walk. Then, it demonstrates how a diffusion-driven instability analysis can be used to derive a set of conditions for chemotactic instabilities in a basic model. Also, it will simulate a specific system in MATLAB to show that the model can generate a variety of complex spatial-temporal patterns. After that, we will apply the chemotaxis models to the specific biological example of forager-scrounger systems. Based on these results, this thesis will suggest new research ideas to extend the forager-scrounger-prey model to examine the behaviour of the patterns for these interactions system. The final results show that the forager-scrounger-prey model is able to generate oscillating spatiotemporal patterns only, with limitation on the size of taxis coefficients, otherwise, the patterns disappear.