Species interaction and reaction diffusion chemical networks
The first part of the project deals with trying to understand the final species composition in ecological communities consisting of species competing for existence in an environment consisting of limited resources. It is assumed that there is a certain fixed dominance relation between any two different species in the community. The dynamics of such communities can be easily modelled using reaction diffusion networks. Although it is known that the final species composition as well as their relative abundance can be determined using concepts from game theory, the reason for the eventual extinction of some of the species within the network is not well understood. We aim to provide a theoretical explanation for the extinction of certain species in such networks. Since numerical methods, in particular implicit schemes are used in order to simulate reaction diffusion networks that model species interactions, in the second part of the project, we determine conditions for the unconditional stability of some well-known implicit numerical schemes that can be employed for simulating the networks.