Dynamic Spatial Interaction Models
New Directions
Bibliographic Data
| ID | 4138940 |
|---|---|
| Authors | Peter Nijkamp (0000-0002-4068-8132, University of Amsterdam), Aura Reggiani (0000-0002-8288-2187, University of Bergamo) |
| Year | 1988 |
| Volume | 20 |
| Issue | 11 |
| Pages | 1449-1460 |
| Publication date | 1988-11-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Environment and Planning A Economy and Space (JOURNAL) |
| Journal identifiers | ISSN: 0308-518X • E-ISSN: 1472-3409 |
| Publisher | SAGE Publications Inc (PUBLISHER) |
| DOI | 10.1068/a201449 |
| OpenAlex | W1972545574 |
| Language | EN |
| Citations received | 5 |
| References cited | 29 |
Spatial interaction models have received a great deal of attention in the past decade. In recent years, various approaches have also been developed to take into account dynamic aspects of spatial interaction models, by means of, for instance, optimal control theory, bifurcation theory, or catastrophe theory. The present paper deals with new directions in dynamic spatial interaction research. The focus is on a general dynamic interaction model analyzed in the framework of optimal control theory. The objective function used is a bicriterion utility model, to be maximized subject to a set of differential equations which bear some resemblance to those used by Wilson in a shopping-centre context. The link between the model presented and a catastrophe type of model is investigated. It is demonstrated that catastrophe behaviour may emerge as a particular case of this optimal control model. Finally, it is shown how external influences (for example, stochastic impacts of the Brownian motion type) affect the optimal trajectory
Catastrophe theory · Differential equation · Interaction model · Mathematical optimization · Optimal control · Ordinary differential equation · Physics · Trajectory · Complex Systems and Time Series Analysis · Computer Science · Engineering · Mathematics · Transportation Planning and Optimization · Urban Design and Spatial Analysis
Contributions by Italian scholars to regional science
The spatial structure debate in spatial interaction modeling
An extended family of spatial interaction models
Logit Models and Chaotic Behaviour
Equilibrium and Nonequilibrium Statistical Thermodynamical Approaches to Modeling Spatial Interaction Dynamics
Concepts and Models of a Quantitative Sociology
Individual decision‐making in dynamic collective systems
An Analysis of Migratory Systems
A Stochastic Version of the Urban Retail Model
The Dynamics of Urban Spatial Structure
On Sudden Urban Growth
Urban Dynamics and Urban Cycles
On Population Growth of Cities in a Region
Economies of Scale and the Existence of Supply-Side Equilibria in a Production-Constrained Spatial-Interaction Model
The Cusp Catastrophe in the Urban Retail Model
Equilibrium Values and Dynamics of Attractiveness Terms in Production-Constrained Spatial-Interaction Models
Equilibria of a Gravity Demand Model
An Analysis of Migratory Systems
| Unique citing works | 5 |
|---|---|
| Citations per year | 0,14 |
| Citation span | 1990 - 2020 (31) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 5 |