© 2012 – Routledge
Mathematical models have long been used by geographers and regional scientists to explore the working of urban and regional systems, via a system where the equilibrium point changes slowly and smoothly as the parameters change slowly and smoothly. However, this all changed with the advent of catastrophe theory and bifurcation, which enabled the development of models where a quite sudden change in the position of the equilibrium point results from a slow, small, smooth change in one or more parameters.
First published in 1981, this reissue of Professor Wilson’s classic study outlines the implications of these mathematical models for geography and regional science, by way of a survey of contemporary applications.
‘An excellent book … His exposition treads the fine line with great care and honesty, telling the reader exactly where imaginative and provocative speculation begin, where well-thought-out "recasting" of previous ideas are solidly based. A major strength is the way Wilson has integrated text and diagram – even a reader without much mathematical background will be able to "see" the ideas.’ – Peter R. Gould
1. A Lay guide to the Mathematics of Catastrophe Theory 2. Differential Equations and Bifurcation Theory 3. Applications of Dynamical Systems Theory: A Survey of Approaches 4. Macro-Scale Applications 5. Bifurcation at the Meso-Scale I: Comparative Statistics of Urban Spatial Structure 6. Bifurcation at the Meso-Scale II: The Dynamics of Urban Spatial Structure 7. Micro-Scale Applications 8. Applications in Other Disciplines and Some New Results for Urban Systems.