A Numerical Study of Diffusive Predator-Prey System with Autotaxis and Non-linear Convection

This project will apply advanced numerical methods to study a real-world ecological problem of high theoretical and practical importance, such as mechanisms of spatiotemporal pattern formation in ecological communities. Spatial distribution of ecological populations is very rarely homogeneous. Species heterogeneity is a common phenomenon observed on various spatial scales, and it has profound implications for ecosystems dynamics. However, its origin is poorly understood and the corresponding underlying mechanisms often remain obscure. The aim of the project is to enhance understanding of the role that directional motion of individuals (e.g., autotaxis or convection) plays in ecological pattern formation. While considerable progress has been made in identification scenarios of pattern formation in diffusive systems, i.e. under approximation of random individual motion, the question about possible impact of directional motion is largely open. One reason for that is that systems of partial differential equations with convective terms are much more difficult for numerical study. Effective numerical methods have appeared only recently and in this project they will be applied to the problem of pattern formation in relevant mathematical models of population dynamics.

A successful candidate must have an UNDERGRADUATE DEGREE IN MATHEMATICS where the curriculum includes modules in ordinary and partial differential equations and in numerical methods. Basic knowledge of programming is also required.