IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

Dynamic spatial interaction models: new directions

  • P Nijkamp
  • A Reggiani

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.envplan.com/abstract.cgi?id=a201449
File Function: abstract
Download Restriction: Fulltext access restricted to subscribers, see http://www.envplan.co.uk/A.html for details

File URL: http://www.envplan.com/epa/fulltext/a20/a201449.pdf
File Function: main text
Download Restriction: Fulltext access restricted to subscribers, see http://www.envplan.co.uk/A.html for details

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Pion Ltd, London in its journal Environment and Planning A.

Volume (Year): 20 (1988)
Issue (Month): 11 (November)
Pages: 1449-1460

as
in new window

Handle: RePEc:pio:envira:v:20:y:1988:i:11:p:1449-1460
Contact details of provider: Web page: http://www.pion.co.uk

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. J R Beaumont & M Clarke & A G Wilson, 1981. "The dynamics of urban spatial structure: some exploratory results using difference equations and bifurcation theory," Environment and Planning A, Pion Ltd, London, vol. 13(12), pages 1473-1483, December.
  2. Fischer, Manfred M. & Nijkamp, Peter, 1987. "From static towards dynamic discrete choice modelling : A State of the Art Review," Regional Science and Urban Economics, Elsevier, vol. 17(1), pages 3-27, February.
  3. J F Kaashoek & A C F Vorst, 1984. "The Cusp Catastrophe in the Urban Retail Model," Environment and Planning A, SAGE Publishing, vol. 16(7), pages 851-862, July.
  4. P K Sikdar & Karmeshu, 1982. "On population growth of cities in a region: a stochastic nonlinear model," Environment and Planning A, Pion Ltd, London, vol. 14(5), pages 585-590, May.
  5. B Harris & A G Wilson, 1978. "Equilibrium values and dynamics of attractiveness terms in production-constrained spatial-interaction models," Environment and Planning A, Pion Ltd, London, vol. 10(4), pages 371-388, April.
  6. M Clarke & A G Wilson, 1981. "The Dynamics of Urban Spatial Structure: Some Exploratory Results Using Difference Equations and Bifurcation Theory," Environment and Planning A, SAGE Publishing, vol. 13(12), pages 1473-1483, December.
  7. B Harris & J-M Choukroun & A G Wilson, 1982. "Economies of scale and the existence of supply-side equilibria in a production-constrained spatial-interaction model," Environment and Planning A, Pion Ltd, London, vol. 14(6), pages 823-837, June.
  8. A C F Vorst, 1985. "A stochastic version of the urban retail model," Environment and Planning A, Pion Ltd, London, vol. 17(12), pages 1569-1580, December.
  9. P K Sikdar & P K Karmeshu, 1982. "On Population Growth of Cities in a Region: A Stochastic Nonlinear Model," Environment and Planning A, SAGE Publishing, vol. 14(5), pages 585-590, May.
  10. R H Day, 1985. "Dynamical systems theory and complicated economic behavior," Environment and Planning B: Planning and Design, Pion Ltd, London, vol. 12(1), pages 55-64, January.
  11. B Harris & A G Wilson, 1978. "Equilibrium Values and Dynamics of Attractiveness Terms in Production-Constrained Spatial-Interaction Models," Environment and Planning A, SAGE Publishing, vol. 10(4), pages 371-388, April.
  12. Rijk, F. J. A. & Vorst, A. C. F., 1983. "Equilibrium points in an urban retail model and their connection with dynamical systems," Regional Science and Urban Economics, Elsevier, vol. 13(3), pages 383-399, August.
  13. B Harris & J-M Choukroun & A G Wilson, 1982. "Economies of Scale and the Existence of Supply-Side Equilibria in a Production-Constrained Spatial-Interaction Model," Environment and Planning A, SAGE Publishing, vol. 14(6), pages 823-837, June.
  14. I Chudzynska & Z Slodkowski, 1984. "Equilibria of a gravity demand model," Environment and Planning A, Pion Ltd, London, vol. 16(2), pages 185-200, February.
  15. Barentsen, W. & Nijkamp, P., 1986. "Modelling non-linear processes in time and space," Serie Research Memoranda 0050, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  16. R H Day, 1985. "Dynamical Systems Theory and Complicated Economic Behavior," Environment and Planning B, SAGE Publishing, vol. 12(1), pages 55-64, March.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:pio:envira:v:20:y:1988:i:11:p:1449-1460. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Neil Hammond)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.