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Dynamic spatial interaction models: new directions

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  • P Nijkamp
  • A Reggiani

Abstract

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.

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Bibliographic Info

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

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

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Handle: RePEc:pio:envira:v:20:y:1988:i:11:p:1449-1460

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References

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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.:
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  1. Nijkamp, P. & Reggiani, A., 1986. "Analysis of dynamic spatial interaction models by means of optimal control," Serie Research Memoranda 0051, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  2. P Kanaroglou & K-L Liaw & Y Y Papageorgiou, 1986. "An analysis of migratory systems: 2. Operational framework," Environment and Planning A, Pion Ltd, London, vol. 18(8), pages 1039-1060, August.
  3. Fischer, M.M. & Nijkamp, P., 1987. "From static towards dynamic discrete choice modelling : a state of the art review," Serie Research Memoranda 0061, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Nijkamp, P. & Reggiani, A., 1987. "Spatial interaction and input-output models : a dynamic stochastic multi-objective framework," Serie Research Memoranda 0059, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  13. De Palma, Andre & Lefevre, Claude, 1985. "Residential change and economic choice behavior," Regional Science and Urban Economics, Elsevier, vol. 15(3), pages 421-434, August.
  14. G J Papageorgiou, 1980. "On sudden urban growth," Environment and Planning A, Pion Ltd, London, vol. 12(9), pages 1035-1050, September.
  15. P Kanaroglou & K-L Liaw & Y Papageorgiou, 1986. "An analysis of migratory systems: 1. Theory," Environment and Planning A, Pion Ltd, London, vol. 18(7), pages 913-928, July.
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Citations

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Cited by:
  1. Nijkamp, P. & Poot, J., 1991. "Lessons from non-linear dynamic economics," Serie Research Memoranda 0105, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  2. Nijkamp, P. & Reggiani, A., 1990. "Spatio-temporal processes in dynamic logit models," Serie Research Memoranda 0063, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  3. Nijkamp, P. & Reggiani, A., 1992. "Static and dynamic spatial interaction models : an integrating perspective," Serie Research Memoranda 0052, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  4. Nijkamp, P. & Reggiani, A., 1990. "Strategic long-term transportation planning and dynamic transportation models : a life cycle interpretation," Serie Research Memoranda 0062, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  5. Nijkamp, P. & Reggiani, A., 1989. "Logit models and chaotic behaviour," Serie Research Memoranda 0054, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  6. Nijkamp, P. & Reggiani, A., 1992. "Non linear evolution of dynamic spatial systems : lessons from chaos and niche theory," Serie Research Memoranda 0066, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  7. Nijkamp, Peter & Reggiani, Aura, 1995. "Non-linear evolution of dynamic spatial systems. The relevance of chaos and ecologically-based models," Regional Science and Urban Economics, Elsevier, vol. 25(2), pages 183-210, April.

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