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Parametrical regulation af economic growth on the basis of mathematical model with the account of foreign commerce

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper is devoted to the application of the theory of parametrical regulation offered by the authors to tasks of maintenance of economic growth with the account of foreign commerce. In the report the mathematical model of economic system of the country is given in view of specified influence. The factors of the mathematical model considered have been evaluated as a result of solving a task of parametrical identification on the statistical data of national economics of the Republic of Kazakhstan and the Russian Federation. The weak structural stability of the specified mathematical model in a compact of eight-dimensional Euclidean space of the phase variables without parametrical regulation has been proved. The proof is based on results of C. Robinson work about structural stability on manifolds with boundary. The methods of the parametrical regulation theory determine the optimum laws of parametrical regulation of processes of economic growth of the Republic of Kazakhstan. These optimum laws are as extremals of the appropriate of variational calculus task at their choice in environment of the given finite set of algorithms. The specified algorithms represent dependences of these or those parameters of mathematical model on some endogenous variables. The dependences of the found laws on influence of two unguided parameters - interest rates on deposits of bank system of the Republic of Kazakhstan and currency exchange rate are being investigated. These dependences are presented as graphs of the criterion's (gross domestic product) optimal values on the parameters of interest rates on deposits and currency exchange rate. The specified graph determines the set of bifurcation points of this two-dimensional parameter. Also, the weak structural stability of the mathematical model with parametrical regulation has been proved.
Czasopismo
Rocznik
Strony
101--106
Opis fizyczny
Bibliogr. 12 poz., wykr.
Twórcy
autor
  • Institute of Informatics and Control Problems, Pushkin str., 125, 050010 Almaty, Republic of Kazakhstan, ashimov@ipic.kz
Bibliografia
  • [1] Anosov D.V., Rough systems, Proceedings of the USSR Academy of Sciences' Institute of Mathematics, Vol. 169, 1985, pp. 59-96, (in Russian).
  • [2] Ashimov A., Borovskiy Yu., Ashimov As., Parametrical Regulation Methods of the Market Economy Mechanisms, Systems Science, Vol. 35, No. 1, 2005, pp. 89-103.
  • [3] Ashimov A., Borovskiy Yu., Ashimov As., Volobueva O., On the choice of the effective laws of parametrical regulation of market economy mechanisms, Automatics and Telemechanics, No. 3, 2005, pp. 105-112, (in Russian).
  • [4] Ashimov A., Sagadiyev K., Borovskiy Yu., Iskakov N., Ashimov As., Parametrical regulation of nonlinear dynamic systems development, Proceedings of the 26th IASTED International Conference on Modelling, Identification and Control, Innsbruck, Austria, 2007, pp. 212-217.
  • [5] Ashimov A., Sagadiyev K., Borovskiy Yu., Iskakov N., Ashimov As., Elements of the market economy development parametrical regulation theory, Proceedings of the Ninth IASTED International Conference on Control and Applications, Montreal, Quebec, Canada, 2007, pp. 296-301.
  • [6] Ashimov A., Sagadiyev K., Borovskiy Yu., Iskakov N., Ashimov As., On the market economy development parametrical regulation theory, Proceedings of the 16th International Conference on Systems Science, Wrocław, Poland, 2007, pp. 493-502.
  • [7] Ashimov A., Sagadiyev K., Borovskiy Yu., Ashimov As., On Bifurcation of Extremals of one Class of Variational Calculus Tasks at the Choice of the Optimum Law of Parametrical Regulation of Dynamic Systems, Proceedings of Eighteenth International Conf. On Systems Engineering, Coventry University, 2006, pp. 15-19.
  • [8] Gukenheimer J., Cholmes P., Nonlinear fluctuations, dynamic systems and bifurcations of vector fields, Institute of Computer Researches, Moscow-Izhevsk, 2002, (in Russian).
  • [9] Matrosov V.M., Chrustalyov M.M., Arnautov O.V., Krotov V.F., On the highly aggregate model of development of Russia, Proceedings of the 2nd International Conference „Analysis of instability development based on mathematical modeling”, Moscow, 1992, pp. 182-243, (in Russian).
  • [10] Petrov A., Pospelov I., Shananin A., Experience of mathematical modeling of economy, Energoatomizdat, Moscow, 1996, (in Russian).
  • [11] Pontryagin A., The ordinary differential equations, Nauka, Moscow, 1970, (in Russian).
  • [12] Robinson C., Structural Stability on Manifolds with Boundary, Journal of differential equations, No. 37, 1980, pp. 1-11.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0062-0013
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