Mathematical Models of Development

  • Viktor V. Ivanov
Part of the Applied Optimization book series (APOP, volume 28)


According to the examples of ES and ES structure (see Ch. 1), mathematical models (MM) of ES or development are introduced. These MM are exact by definition and different from each other depending on interpretation and the extent of detailing or collection. Some additional MM are introduced concerning the fiscal side of human activities for AES and the natural balance relations for NES. A comparison with the well-known MM is considered. The problem of estimating input data and the problem of MM completeness are analyzed. Statements of other problems are given.


Maximization Problem Work Place Elementary Index Linear Stationary System Monotone Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Astrom K.J., EykhoffP., System Identification–A Survey, Automatica, 7, 1971, 123–167.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Baglay R.D., Smirnov K.K, Handling Two Dimensional Signals on Computers, ZVMiMF, 15, N 1, 1975, 241–247 (in Russian).Google Scholar
  3. 3.
    Bethea R.M., Duran B.S., Boullion T.L., Statistical Methods for Engineers and Scientists, Decker, 1975, 583 pp.Google Scholar
  4. 4.
    Girlin S.K., Ivanov V.V., Modeling of Developing Systems Interaction, DAN Ukr.SSR, N 1, 1986, 58–60 (in Ukrainian).MathSciNetGoogle Scholar
  5. 5.
    Glushkov V.M, On a Class of Dynamic Macroeconomic Models, Upravlyayushchie. Sistemy and Mashiny, 2, 1977, 3–6 (in Russian).Google Scholar
  6. 6.
    Glushkov V.M., Ivanov V.V., JanenkoV.M., One Class of Nonlinear Dynamic Models and Its Applications, Physica, 2D, 1981, 61–72.MATHGoogle Scholar
  7. 7.
    Glushkov V.M, Ivanov V.V., Janenko V.M., Developing Systems Modeling, M.: Nauka, 1983, 352 pp. (in Russian).MATHGoogle Scholar
  8. 8.
    Glushkov V.M., Pshenichnyj B.N., On Mathematical Models of Economic Growth, Cybernetics, 13,N4, 1977, 1–6.Google Scholar
  9. 9.
    Hritonenko N., Yatsenko Yu., Modeling and Optimization of the Lifetime of Technologies, Kluwer Academic Publishers, 1996, xxxvi + 250 pp.Google Scholar
  10. 10.
    Ivanov V.V., Systems Development Simulation Problems and C. Caratheodoiy’s Concepts, in the book: Constantin Caratheodory: An International Tribute, World Science., 1, 1991, 501–526.Google Scholar
  11. 11.
    Ivanov V.V., Yatsenko Yu.P., Galiev U.E., Comparison of Some Integral Macroeconomic Models, Avtomatika, 4, 1986, 47–53 (in Russian).Google Scholar
  12. 12.
    Kantorovich L.V., Gor*kov L.I., On Functional Equations under Analysis of One-Product Economic Model, DAN SSSR, 129, N 4, 1959, 732–736 (in Russian).MATHGoogle Scholar
  13. 13.
    Kantorovich L.V., Zhiyanov V.I., One-Product Dynamic Model of Economy Considering Variation of Fund Structure under Technical Progress, DAN SSSR, 211, N 6, 1973, 1280–1283 (in Russian).Google Scholar
  14. 14.
    Krasnoshchokov P.S., Petrov A.A., Principles of Model Construction, Moscow Univ., 1983, 264 pp. (in Russian).Google Scholar
  15. 15.
    Law, Dornald’s Illustrated Medical Dictionary, W. B. Saunders Co., 1988, 899–902.Google Scholar
  16. 16.
    Malcomson J.M., Replacement and the Rental Value of Capital Equipment Subject to Obsolescence, Journal of Economic Theory, 10, 1975, 24–41.MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Petrov A. A., Pospelov I.G., Systematic Analysis of Developing Economy, Izv. AN SSSR, Techn. kibernetika, 1979, N 2,18–27; N 3,28–38; N 4,11–23; N 5, 13–24 (in Russian).MathSciNetGoogle Scholar
  18. 18.
    Poluectov R.A., Pykh Yu.A., Shvytov I A, Dynamic Model of Ecological Systems, L.: Gidrometioizdat, 1980, 288 pp. (in Russian).Google Scholar
  19. 19.
    Riflein J., The Biotech Century, Penguin Putnam Inc., 1998, 272 pp.Google Scholar
  20. 20.
    Sharpe F.R., Lotka A.J., A Problem in Age-Distribution, Philos. Mag., 21, 1911, 435–438.CrossRefMATHGoogle Scholar
  21. 21.
    Smith H.L., Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, vol. 41, AMS, 1995, x+174 pp.Google Scholar
  22. 22.
    Solow R, Investment and Technical Progress, Stanford Univ. Press, 1960, 89–104.Google Scholar
  23. 23.
    Thermodynamic Principles, McGraw-Hill Encyclopedia of Science Technology, Vol. 13, 1982, 645–650.Google Scholar
  24. 24.
    Webb G., Theory of Nonlinear Age Dependant Population, Decker, 1985, 294 pp.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Viktor V. Ivanov
    • 1
    • 2
  1. 1.Glushkov Institute of CyberneticsKievUkraine
  2. 2.University of South FloridaTampaUSA

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