Approaches to Geo-mathematical Modelling

Chapter 1The Toolkit

Alan G. Wilson

Geographical systems are characterised by locations, activities at locations, interactions between them and the infrastructures that carry these activities and flows. They can be described at a great variety of scales, from individuals, organisations and buildings, through neighbourhoods, to towns and cities, regions and countries. There is an understanding, often partial, of these entities, and in many case this understanding is represented in theories which in turn are represented in mathematical models. We can characterise these models, with geography as a core, as geo-mathematical models.

In this book, our main examples are models that represent elements of the global system covering such topics as trade, migration, security and development aid. We also work with examples at finer scales. We review this set of models, along with some outstanding research questions, in order to demonstrate how they now form, between them, an effective toolkit that can be applied not only to particular global systems but more widely in the modelling of complex systems.

These examples have been developed in the context of an EPSRC-funded complexity science programme with twin foci: developing new tools and applying these to real-world problems. In presenting the ‘tools’ here, it is useful to be aware of Weaver's distinction between systems of disorganised complexity and systems of organised complexity. Both kinds of systems have large numbers of elements, ...