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original: Settlement formation models with entropy operator

Author

Listed:
  • Vladimir I. Shvetsov

    (Institute for System Analysis, Moscow, Russia)

  • Wolfgang Weidlich

    (Institute of Theoretical Physics, Stuttgart University, D-70550 Stuttgart, Germany)

  • Yury S. Popkov

    (Institute for System Analysis, Moscow, Russia)

Abstract

An integrated dynamical model of the settlement formation is presented. The model may be considered as a modification of Weidlich-Munz model (1988), which focussed on the interaction between the population migration and the economical activity and its role for the processes of self-organization in the spatial structure of settlements. In the present model the detailed description of the economical subsystem is implemented on the basis of the theory of economical growth in a fully dynamical manner. The stochastic commodity exchange processes are described in the frame of the macrosystem approach, which uses an entropy maximization procedure. Some qualitative features of the model are investigated. It is shown in particular, that the homogeneous equilibrium distribution of poupulation and economy is unstable under certain conditions. This leads to the development of non-homogeneous spatial structures from the initially homogeneous state.

Suggested Citation

  • Vladimir I. Shvetsov & Wolfgang Weidlich & Yury S. Popkov, 1998. "original: Settlement formation models with entropy operator," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 32(2), pages 267-294.
    • Handle: RePEc:spr:anresc:v:32:y:1998:i:2:p:267-294
    Note: Received: September 1995 / Accpeted in revised form: May 1997
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    Cited by:

    1. Yuri S. Popkov, 2021. "Controlled Positive Dynamic Systems with an Entropy Operator: Fundamentals of the Theory and Applications," Mathematics, MDPI, vol. 9(20), pages 1-19, October.
    2. Popkov, Alexey Y. & Popkov, Yuri S. & van Wissen, Leo, 2005. "Positive dynamic systems with entropy operator: Application to labour market modelling," European Journal of Operational Research, Elsevier, vol. 164(3), pages 811-828, August.
    3. Yuri S. Popkov, 2020. "Equilibria and Stability of One Class of Positive Dynamic Systems with Entropy Operator: Application to Investment Dynamics Modeling," Mathematics, MDPI, vol. 8(6), pages 1-15, May.

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