Harris and Wilson (1978) Model Revisited: The Spatial Period‐doubling Cascade in an Urban Retail Model

Osawa, Minoru; Akamatsu, Takashi; Takayama, Yuki

doi:10.1111/jors.12306

Cited by 22 publications

(14 citation statements)

References 44 publications

(107 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our model is based on the Boltzmann-Lotka-Volterra (BLV) method [18,19,20,21]. The BLV models involve two components: a fast equilibration, "Boltzmann", component and a slow dynamic, "Lotka-Volterra", component.…”

Section: Introductionmentioning

confidence: 99%

On critical dynamics and thermodynamic efficiency of urban transformations

2018

View full text Add to dashboard Cite

Urban transformations within large and growing metropolitan areas often generate critical dynamics affecting social interactions, transport connectivity and income flow distribution. We develop a statistical–mechanical model of urban transformations, exemplified for Greater Sydney, and derive a thermodynamic description highlighting critical regimes. We consider urban dynamics at two time scales: fast dynamics for the distribution of population and income, modelled via the maximum entropy principle, and slower dynamics evolving the urban structure under spatially distributed competition. We identify phase transitions between dispersed and polycentric phases, induced by varying the social disposition—a factor balancing the suburbs’ attractiveness—in contrast with the travel impedance. Using the Fisher information, we identify critical thresholds and quantify the thermodynamic cost of urban transformation, as the minimal work required to vary the underlying parameter. Finally, we introduce the notion of thermodynamic efficiency of urban transformation, as the ratio of the order gained during a change to the amount of required work, showing that this measure is maximized at criticality.

show abstract

Section: Introductionmentioning

confidence: 99%

On critical dynamics and thermodynamic efficiency of urban transformations

2018

View full text Add to dashboard Cite

show abstract

“…The temporal stability of the migration flows is a crucial element of our long-term analysis. Despite being consistent within the period of observation (2006–2016), they may be affected by multiple factors in future: Human migration is a complicated non-linear process involving multiple interdependent factors, often leading to various phase transitions and critical phenomena [ 19 , 20 , 22 , 27 , 43 , 56 , 57 ]. However, the relocation data may contain some unique features that are not captured in other static human mobility and land-use data (e.g., [ 13 , 19 , 24 , 27 , 58 ]).…”

Section: Discussionmentioning

confidence: 99%

Diffusive Resettlement: Irreversible Urban Transitions in Closed Systems

Slavko

Prokopenko

Glavatskiy

2021

Entropy

View full text Add to dashboard Cite

We propose a non-equilibrium framework for modelling the evolution of cities, which describes intra-urban migration as an irreversible diffusive process. We validate this framework using the actual migration data for the Australian capital cities. With respect to the residential relocation, the population is shown to be composed of two distinct groups, exhibiting different relocation frequencies. In the context of the developed framework, these groups can be interpreted as two components of a binary fluid mixture, each with its own diffusive relaxation time. Using this approach, we obtain long-term predictions of the cities’ spatial structures, which define their equilibrium population distribution.

show abstract

“…There is a lot of complexity in the dynamics which are controlled by a system of nonlinear simultaneous differential equations. Progress has been made in terms of analysing the number of solutions in the state space of a BLV model [22] as well as particular kinds of bifurcations [23]. There are many other models in the complete family of BLV-models including house price dynamics and housing provision dynamics [24].…”

Section: Dynamic Urban Models and The Blv Approachmentioning

confidence: 99%

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

et al. 2019

View full text Add to dashboard Cite

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 (two-zone and three-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 categorise two causes of phase transition of urban development: (A) change in variable values (e.g., building a new shopping centre) that cause the system to cross a basin boundary, (B) 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.

show abstract

Harris and Wilson (1978) Model Revisited: The Spatial Period‐doubling Cascade in an Urban Retail Model

Cited by 22 publications

References 44 publications

On critical dynamics and thermodynamic efficiency of urban transformations

On critical dynamics and thermodynamic efficiency of urban transformations

Diffusive Resettlement: Irreversible Urban Transitions in Closed Systems

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

Contact Info

Product

Resources

About