Hard and soft mathematical models and their applications

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Ohirko I. V., Yasinska-Darmi L. M., Yasinskyi M. F. № 1 (50) 107-122 Image Image

One of important scientific problems of natural history is to solve a task of foresight of the probed object conduct in time and space on the basis of certain knowledge about its initial state. This task has been taken to find some law which allows to define the object future in any moment of time of t>t0 with the initial moment of time of t0 in the point of space of x0. Depending on the degree of the object complication the law can be determined or probable, it can describe the evolution of object only in time, only in space, and can describe a spatial-temporal evolution. Under the dynamic system they understand any object or process, for which a simple certain concept of state as some totality of values has been determined in this moment of time, and the law which describes time history (evolution) of the initial state has been set. The mathematical model of the dynamic system is considered to be set if the system parameters (coordinates) have been introduced to determine its state simply, and the law of evolution has been detected. Depending on the degree of approaching, different mathematical models can be put in accordance with the same system.

Keywords: system, dynamic systems, soft systems, hard systems, linear operator.

  • 1. Bertalanfi L. (1969), General theory of systems: a review of problems and results, Systematic researches: Annual, Science, pp. 30–54.
  • 2. Uyemov A. I. (1978), Systematic approach and general theory of systems, World, Moscow.
  • 3. Zgurovskyi M., Dobronogov A.V. and Pomerantseva T. (1977), Research of social processes on the basis of the system analysis methodology, Scientific idea, Moscow.
  • 4. Klir J. (1990), Systemology, Automation of the system problems solution, Radio and connection, Moscow.
  • 5. Laszlo E. (1972), Introduction to systems philosophy: Toward a new paradigm of the contemporary thought, Harper and Row, New York.
  • 6. Plotynskyi M. Yu. (1992), Mathematical design in the social processes dynamics, MSU Press, Moscow.
  • 7. Strashkraba M. and Gnauk A. (1989), Fresh water ecosystems. Mathematical design, World, Moscow.
  • 8. Vartovskyi M. (1988), Models. Representation and scientific understanding, Progress, Moscow.
  • 9. Vunsh G. (1978), Theory of systems, Soviet radio, Moscow.
  • 10. Jeffers J. (1981), Introduction to the system analysis: application in ecology, World, Moscow.
  • 11. Neyman J. and Morgershtern O. (1970), Theory of games and economic conduct, Science, Moscow.
  • 12. Williams J. (1960), Perfect strategist or the ABC on the strategic game theory, Soviet radio, Moscow.
  • 13. Karlin S. (1964), Mathematical methods in the theory of games, programming and eco­nomy, World, Moscow.
  • 14. Eyres P. (1971), Scientific and technical prognosis and long-term planning, World, Moscow.
  • 15. Saati T. (1989), Mathematical models of conflict situations, Soviet radio, Moscow.
  • 16. Kolyada Yu.V. and Semashko K.A. (2012), The «Soft» design of coexistence of legal and shadow economies of society, Problems of the transformational economics, Proceedings of the 4th All-Ukrainian scientific practical conference, ZNU Press, March 23d , Kryvyi Rih, pp. 36–38.
  • 17. Experience of social processes design modelling (1989), in Paniotto V I. (Ed.), Scientific idea, Kyiv.
  • 18. Ivakhnenko A. G. (1990), Continuity and discreteness, Scientific idea, Kyiv.
  • 19. Van Gyg J. (1981), General applied theory of systems, Vol.1,2, World, Moscow.
  • 20. Checland R.V. (1988), Soft systems methodology: a review, Applied System Analysis Journal, Vol.15, No. 1, pp. 27–36.
  • 21. Bartolomju D. (1985), Stochastic models of social processes, Finances and statistics, Moscow.
  • 22. Barucha-Ryd A. T. (1969), Elements of the Markov processes theory and their application, Science, Moscow.
  • 23. Roberts F. S. (1986), Discrete mathematical models concerning social, biological and economic tasks, Science, Moscow.
  • 24. Khaken G. (1980), Synergetics, World, Moscow.