The Analysis of Bifurcation Phenomena Associated with the Evolution of Urban Spatial Structure

M. Clarke and A. G. Wilson
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M. Clarke: University of Leeds, School of Geography
A. G. Wilson: University of Leeds, School of Geography

A chapter in Bifurcation Analysis, 1985, pp 67-99 from Springer

Abstract: Abstract One of the more interesting developments in urban and regional modelling in recent years has been the analysis of the bifurcation properties of a wide variety of models. Just as Jay Forrester’s (1969) attempts to explicitly focus on urban dynamics provided the impetus for those within the modelling discipline to move away from purely static analysis, the innovative work of Thorn, Zeeman and others has brought the notion of bifurcation behaviour to the notice of those currently engaged in urban modelling. In this paper we outline how we have attempted to analyse the bifurcation properties of a well-known set of spatial interaction and activity models, both in their equilibrium and disequilibrium formulations. In addition, we give a number of illustrations of numerical simulations performed for both a 729-zone hypothetical system and also a 30 x 900 Leeds system where we explicitly focus on the problem of modelling urban spatial structure. (A much fuller set of results can be found in Clarke and Wilson, 1984).

Keywords: Equilibrium Point; Bifurcation Point; Bifurcation Theory; Catastrophe Theory; Urban Structure (search for similar items in EconPapers)
Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-6239-2_5

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DOI: 10.1007/978-94-009-6239-2_5

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