摘要：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.
关键词：dynamic urban modeling; Boltzmann–Lotka–Volterra retail model; complex systems; state space; phase transitions; urban development dynamic urban modeling ; Boltzmann–Lotka–Volterra retail model ; complex systems ; state space ; phase transitions ; urban development
