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Rate effects on the growth of centres

Published online by Cambridge University Press:  07 July 2016

H. M. FRY  and
F. T. SMITH
H. M. FRY
Affiliation:
Centre for Advanced Spatial Analysis, University College London, Gower Street, London, United KingdomWC1E 6BT email: [email protected]
F. T. SMITH
Affiliation:
Department of Mathematics, University College London, Gower Street, London, United KingdomWC1E 6BT email: [email protected]
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Abstract

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Entropy maximising spatial interaction models have been widely exploited in a range of disciplines and applications: from trade and migration flows to the spread of riots and the understanding of spatial patterns in archaeological sites of interest. When embedded into a dynamic system and framed in the context of a retail model, the dynamics of centre growth poses an interesting mathematical problem, with bifurcations and phase changes, which may be addressed analytically. In this paper, we present some analysis of the continuous retail model and the corresponding discrete version, which yields insights into the effect of space on the evolving system, and an understanding of why certain retail centres are more successful than others. The slowly developing growths and the fast explosive growths that are of particular concern are explained in detail.

Keywords

Mathematical modelurban evolutionentropyasymptotics91D1091D2534E1034A3439A33
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 2 , April 2017 , pp. 221 - 242
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2016

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