When attempting to model complex systems (such as those driving social phenomena), there is an inherent trade-off between realism and rigour. Theoretical physicists have traditionally favoured “simple” models with few parameters, rather than more “realistic” models with a large number of parameters. The advantage of this approach is that such models may often be very thoroughly analysed and their behaviours well understood, however, the relevance of such models to the real world are sometimes questioned.
In this project we plan to have a chain of models connecting very detailed descriptive models at one end, to simple abstract models at the other. By approaching the modelling process in this way, we hope to create a bridge between the opposing methodologies of simplicity and realism. Starting from a detailed realistic model, simplifications will be made (and their effects analysed) to create an abstract model which describes the core mechanics of the complex one.
The abstract models investigated may be agent-based, but with the agents having only one or two attributes. The models will be studied using both numerical simulation and mathematical analysis. Spatial versions of these models may be defined on lattices or networks and may involve patches or metapopulations.
Previous work of the group has included modelling evolving networks, analysing and solving neutral theories of biodiversity, constructing models of language change in a speech community and understanding the patterns of cyclical variation in epidemics of childhood diseases.