Mathematical models have long been used by geographers and regional scientists to explore the working of urban and regional systems. However, this all changed with the advent of catastrophe theory and bifurcation. This study outlines the implications of these mathematical models for geography and regional science.
The authors of this book, the first printing of which was published as Volume 5 of the Encyclopaedia of Mathematical Sciences, have given a masterly exposition of these two theories, with penetrating insight.
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 ...
The new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering.
Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977.
The authors of this book, the first printing of which was published as Volume 5 of the Encyclopaedia of Mathematical Sciences, have given a masterly exposition of these two theories, with penetrating insight.
Based on a lecture course, this text gives a rigorous introduction to nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory.
Institut d'Etudes Scientifiques de Carg'ese, Publ. Math. Dept., Univ. ... Goodwin, B. Review of Thom, R. Stabilité Structurelle et Morphogénése. ... Gromoll, D. and Meyer, W. On differentiable functions with isolated critical points.
Explains catastrophe theory, which uses geometric shapes to transform abstract concepts into concrete visual pictures, and cites numerous examples to show its usefulness in dealing with problems in economics, psychology,...
Dynamical systems.
This textbook gives a contemporary account of singularity theory and its principal application, bifurcation theory.