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Dynamic Spatial Interaction Models: New Directions

Author

Listed:
  • P Nijkamp

    (Department of Economics, Free University, PO Box 7161, 1007 MC Amsterdam, The Netherlands)

  • A Reggiani

    (Department of Mathematics, University of Bergamo, Via Salvecchio 19, 24100 Bergamo, Italy)

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.

Suggested Citation

  • P Nijkamp & A Reggiani, 1988. "Dynamic Spatial Interaction Models: New Directions," Environment and Planning A, , vol. 20(11), pages 1449-1460, November.
    • Handle: RePEc:sae:envira:v:20:y:1988:i:11:p:1449-1460
    DOI: 10.1068/a201449
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    References listed on IDEAS

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    1. 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, , vol. 14(6), pages 823-837, June.
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    6. 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.
    7. 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.
    8. A C F Vorst, 1985. "A Stochastic Version of the Urban Retail Model," Environment and Planning A, , vol. 17(12), pages 1569-1580, December.
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    Cited by:

    1. Yang, Chunxia & Tang, Minxuan & Cao, Yongjian & Chen, Yanhua & Deng, Qiangqiang, 2015. "The study on variation of influential regions in China from a perspective of asymmetry economic information flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 180-187.
    2. 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.
    3. repec:elg:eechap:14395_20 is not listed on IDEAS
    4. Peter Nijkamp, 2013. "The Universal Law Of Gravitation And The Death Of Distance," Romanian Journal of Regional Science, Romanian Regional Science Association, vol. 7(2), pages 1-10, DECEMBER.
    5. 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.
    6. 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.

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