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Dynamic spatial interaction models : new directions

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  • Nijkamp, P.

    (Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics)

  • Dieperink, H.

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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Suggested Citation

  • Nijkamp, P. & Dieperink, H., 1987. "Dynamic spatial interaction models : new directions," Serie Research Memoranda 0069, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    • Handle: RePEc:vua:wpaper:1987-69
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    References listed on IDEAS

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    1. J F Kaashoek & A C F Vorst, 1984. "The Cusp Catastrophe in the Urban Retail Model," Environment and Planning A, , vol. 16(7), pages 851-862, July.
    2. 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.
    3. A C F Vorst, 1985. "A Stochastic Version of the Urban Retail Model," Environment and Planning A, , vol. 17(12), pages 1569-1580, December.
    4. 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.
    5. 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.
    6. B Harris & A G Wilson, 1978. "Equilibrium Values and Dynamics of Attractiveness Terms in Production-Constrained Spatial-Interaction Models," Environment and Planning A, , vol. 10(4), pages 371-388, April.
    7. P K Sikdar & P K Karmeshu, 1982. "On Population Growth of Cities in a Region: A Stochastic Nonlinear Model," Environment and Planning A, , vol. 14(5), pages 585-590, May.
    8. 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.
    9. R H Day, 1985. "Dynamical Systems Theory and Complicated Economic Behavior," Environment and Planning B, , vol. 12(1), pages 55-64, March.
    10. 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, , vol. 13(12), pages 1473-1483, 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. repec:elg:eechap:14395_20 is not listed on IDEAS
    3. 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.
    4. 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.
    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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