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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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  • P Nijkamp & A Reggiani, 1988. "Dynamic spatial interaction models: new directions," Environment and Planning A, Pion Ltd, London, vol. 20(11), pages 1449-1460, November.
  • Handle: RePEc:pio:envira:v:20:y:1988:i:11:p:1449-1460
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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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