This is a past event
Dr Fordyce Davidson from Department of Mathematics, University of Dundee will give a very brief overview of a range of topics he has worked on over recent years in the general area of the application and analysis of differential equations. Plus recent work regarding travelling waves in systems of reaction-diffusion equations.
I will give a very brief overview of a range of topics that I worked on over recent years in the general area of the application and analysis of differential equations before concentrating on recent work regarding travelling waves in systems of reaction-diffusion equations.
In this part, I will discuss a class of bistable reaction-diffusion systems used to model the competitive interaction of two species. The interactions are assumed to be of classic "Lotka-Volterra" type and we will consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interplay of relative motility (diffusion) and competitive strength can cause waves of invasion to be halted and reversed.
By establishing rigorous results concerning related degenerate and near-degenerate systems, we build a picture of the dependence of the wave speed on system parameters. Our results lead us to conjecture that this class of competition model has three "zones of response" in which the wave direction is left-moving, reversible and right-moving, respectively and indeed that in all three zones, the wave speed is an increasing function of the relative motility.
- Speaker
- Dr Fordyce Davidson
- Hosted by
- Engineering
- Venue
- TBC