Introduction. In this report, we investigate the population dynamics of species within habitats where we allow migration of the species between the habitats. The majority of this research is focussed on a two-habitat model, a situation that could, for example, occur within neighbouring environments on one side of a river bank.
We are mainly concerned with the long-term behaviour of the populations. In order to understand this, we will look for steady-state solutions where the population size is not changing, and determine their stability.
This work can easily be extended to consider multiple environments in various arrangements, and is thus a broad topic. For example, we could consider six habitats where we allow migration only between neighbouring habitats, between certain habitats or between all of them. Here we lay the important foundation work for considering more complex arrangements and increasing numbers of habitats.
This is an important research problem, since is allows us to investigate how the long term impacts of one environments will affect neighbouring environments. This has particular application to the area of environmental impact studies where we may be altering the habitat of a species.
Most of the calculations and graphing used during this research project have been performed using Maple 8. Whilst most of the graphs are fairly accurate, a more sophisticated graphics package would be useful when using the model in a real-life situation.