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Using the State Space of a BLV Retail Model to Analyse the Dynamics and Categorise Phase Transitions of Urban Development

Joel Dearden, Yi Gong, Mark Jones Orcid Logo, Alan Wilson

Urban Science, Volume: 3, Issue: 1, Start page: 31

Swansea University Author: Mark Jones Orcid Logo

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DOI (Published version): 10.3390/urbansci3010031

Abstract

Urban areas are now the dominant human habitat, with more influence than ever on economies, environment and our health. Dynamic urban models are increasingly applied to explore possible future scenarios of urban development to achieve sustainability. However, it is still challenging to use these mod...

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Published in: Urban Science
ISSN: 2413-8851
Published: MDPI 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa48971
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first_indexed 2019-02-25T15:52:10Z
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spelling 2019-03-21T16:02:46.1571231 v2 48971 2019-02-25 Using the State Space of a BLV Retail Model to Analyse the Dynamics and Categorise Phase Transitions of Urban Development 2e1030b6e14fc9debd5d5ae7cc335562 0000-0001-8991-1190 Mark Jones Mark Jones true false 2019-02-25 SCS Urban areas are now the dominant human habitat, with more influence than ever on economies, environment and our health. Dynamic urban models are increasingly applied to explore possible future scenarios of urban development to achieve sustainability. However, it is still challenging to use these models for prediction, taking into consideration the complex nature of urban systems, the nonlinear interactions between different parts of the system, and the large quantities of data output from simulations. The aim of this study is to analyse the dynamics of two hypothetical dynamic BLV (Boltzmann-Lotka-Volterra) retail models (2-zone and 3-zone). Here, by visualising and analysing the qualitative nature of state space (the space of all possible initial conditions), we propose an alternative way of understanding urban dynamics more fully. This involves examining all possible configurations of an urban system in order to identify the potential development in future. Using this method we are able to identify a supply-demand balancing hyperplane and identify two causes of phase transition of urban development: 1) change in variable values (e.g. building a new shopping centre) that cause the system to cross a basin boundary, 2) state space change (e.g. construction of a new motorway changes travel costs in the region) causes the containing basin to be modified. We also identify key characteristics of the dynamics such as velocity and how the phase space landscape changes over time. This analysis is then linked with equilibrium-size graphs, which allow insights from state space to be applicable to models with large numbers of zones. More generally this type of analysis can potentially offer insights into the nature of the dynamics in any dynamical-systems-type urban model. This is critical for increasing our understanding and helping stakeholders and policy-makers to plan for future urban changes. Journal Article Urban Science 3 1 31 MDPI 2413-8851 11 3 2019 2019-03-11 10.3390/urbansci3010031 https://www.mdpi.com/2413-8851/3/1/31 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2019-03-21T16:02:46.1571231 2019-02-25T09:48:21.3614416 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Joel Dearden 1 Yi Gong 2 Mark Jones 0000-0001-8991-1190 3 Alan Wilson 4 0048971-21032019095742.pdf 2019_UrbanSci.pdf 2019-03-21T09:57:42.1970000 Output 929307 application/pdf Version of Record true 2019-03-20T00:00:00.0000000 Released under the terms of a Creative Commons Attribution License (CC-BY). true eng
title Using the State Space of a BLV Retail Model to Analyse the Dynamics and Categorise Phase Transitions of Urban Development
spellingShingle Using the State Space of a BLV Retail Model to Analyse the Dynamics and Categorise Phase Transitions of Urban Development
Mark Jones
title_short Using the State Space of a BLV Retail Model to Analyse the Dynamics and Categorise Phase Transitions of Urban Development
title_full Using the State Space of a BLV Retail Model to Analyse the Dynamics and Categorise Phase Transitions of Urban Development
title_fullStr Using the State Space of a BLV Retail Model to Analyse the Dynamics and Categorise Phase Transitions of Urban Development
title_full_unstemmed Using the State Space of a BLV Retail Model to Analyse the Dynamics and Categorise Phase Transitions of Urban Development
title_sort Using the State Space of a BLV Retail Model to Analyse the Dynamics and Categorise Phase Transitions of Urban Development
author_id_str_mv 2e1030b6e14fc9debd5d5ae7cc335562
author_id_fullname_str_mv 2e1030b6e14fc9debd5d5ae7cc335562_***_Mark Jones
author Mark Jones
author2 Joel Dearden
Yi Gong
Mark Jones
Alan Wilson
format Journal article
container_title Urban Science
container_volume 3
container_issue 1
container_start_page 31
publishDate 2019
institution Swansea University
issn 2413-8851
doi_str_mv 10.3390/urbansci3010031
publisher MDPI
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
url https://www.mdpi.com/2413-8851/3/1/31
document_store_str 1
active_str 0
description Urban areas are now the dominant human habitat, with more influence than ever on economies, environment and our health. Dynamic urban models are increasingly applied to explore possible future scenarios of urban development to achieve sustainability. However, it is still challenging to use these models for prediction, taking into consideration the complex nature of urban systems, the nonlinear interactions between different parts of the system, and the large quantities of data output from simulations. The aim of this study is to analyse the dynamics of two hypothetical dynamic BLV (Boltzmann-Lotka-Volterra) retail models (2-zone and 3-zone). Here, by visualising and analysing the qualitative nature of state space (the space of all possible initial conditions), we propose an alternative way of understanding urban dynamics more fully. This involves examining all possible configurations of an urban system in order to identify the potential development in future. Using this method we are able to identify a supply-demand balancing hyperplane and identify two causes of phase transition of urban development: 1) change in variable values (e.g. building a new shopping centre) that cause the system to cross a basin boundary, 2) state space change (e.g. construction of a new motorway changes travel costs in the region) causes the containing basin to be modified. We also identify key characteristics of the dynamics such as velocity and how the phase space landscape changes over time. This analysis is then linked with equilibrium-size graphs, which allow insights from state space to be applicable to models with large numbers of zones. More generally this type of analysis can potentially offer insights into the nature of the dynamics in any dynamical-systems-type urban model. This is critical for increasing our understanding and helping stakeholders and policy-makers to plan for future urban changes.
published_date 2019-03-11T03:59:41Z
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