Wyniki wyszukiwania - Biblioteka Nauki

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On bifurcation of extremals of one class of variational calculus tasks with multiparametrical perturbation

100%

Ashimov A. A. , Sagadiyev K. A. , Borovskiy Y. V. , Iskakov N. A. , Ashimov A. A.

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2007

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tom Vol. 33, no 4

85-91

EN

A bifurcation of the extremals of one variational calculus task on the choice of optimum laws for a parametrical regulation of a dynamic system in the given finite set of algorithms is under consideration. An assertion about conditions sufficient for the existence of the specified variational calculus task's solution is formulated and proved. A defintion of a bifurcation point under a multiparametrical perturbation of the given variational calculus task is provided. An assumption on the sufficient conditions for its existence is formulated and proved. A numerical algorithm of calculating a bifurcation value of a parameter is offered. The findings are illustrated by the example of calculated set of bifurcation points of the extremals of the variational calculus task on the choice of optimum laws for a parametrical regulation of the market economy mechanisms in the given finite set of algorithms on the basis of a mathematical model of the economic system of the country, which is suggested in order to investigate the influence of state expenditures upon its evolution. The research findings could be applied to the process of development and implementation of an effective state economic policy.

2

Parametrical regulation of economic growth on the basis of one-class mathematical models

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Ashimov A. A. , Iskakov N. A. , Borovskiy Y. V. , Sultanov B. T. , Ashimov A. A.

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2009

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tom Vol. 35, no 1

57-63

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 influence of the state's consumer expenses share in gross domestic product on development of economy. In the article, a 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 the task of parametrical identification on the statistical data of national economy of the Republic of Kazakhstan. The weak structural stability of the specified mathematical model in a compact of four-dimensional Euclidean space of the phase variables without parametrical regulation has been proved. The proof is based on results of C. Robinson's 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 laws found on the two unguided parameters, i.e., interest rates on deposits of bank system of the Republic of Kazakhstan and rates of taxes on dividends, are being investigated. These dependences are submitted as corresponding graphs of the criterion's (gross domestic product) optimal values on one and two economic parameters. The appropriate bifurcation points and sets of bifurcation points have been determined on the basis of the graphs obtained. Also, the weak structural stability of the mathematical model with parametrical regulation has been proved.

3

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

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Ashimov A. A. , Isakov N. A. , Borovskiy Y. V. , Sultanov B. T. , Ashimov A. A.

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2009

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tom Vol. 35, no 2

101-106

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.

4

On the theory elements and methods of parametrical regulation of the national economy evolution based on discrete stochastic dynamic models

86%

Ashimov A. A. , Sultanov B. T. , Borovskiy Y. V. , Novikov D. A. , Serovajsky S. Y. , Ashimov A. A.

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2010

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tom Vol. 36, no 4

5-12

EN

The work presents results on development of the parametrical regulation theory for a class of discrete stochastic dynamic systems with additive noise. Within the framework of development of the parametrical regulation theory for discrete dynamic systems we formulated and proved the theorem about sufficient conditions for existence of solutions to the problems of variational calculus on synthesis of optimal laws of parametrical regulation and the theorem about sufficient conditions for continuous dependence of criterions' optimal values of the problem of the values of unregulated parameters. The discrete stochastic model, taken as an example, was obtained from one deterministic computable model of general equilibrium of economic sectors by adding additive noise to the right parts of dynamic equations of the model. The problem of parametrical identification of the deterministic variant of the model was preliminarily solved based on the statistical data for the Republic of Kazakhstan. For the stochastic and deterministic variants of the investigated model problems of optimal economic growth of national economy of the Republic of Kazakhstan were formulated and solved (applying the methods of parametrical regulation theory).

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Development of the parametric regulation theory based on one class of computable general equilibrium models

86%

Ashimov A. A. , Sultanov B. T. , Adilov Z. M. , Borovskiy Y. V. , Borovskiy N. Y. , Ashimov A. A.

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2010

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tom Vol. 36, no 2

5-10

EN

The paper presents some results of the development of parametrical regulation theory elements for computable general equilibrium models (CGE models) taking into consideration peculiarities of such models as well as peculiarities of finding optimum (in the sense of some criterion) values of controlled parameters. The authors prove a statement on the existence of a solution of variation calculus task of finding the upper bound of some criterion for discrete dynamic system. Theoretical results have been obtained by means of applying geometrical methods in variation tasks and methods of the theory of discrete dynamic systems. Efficiency of application of the parametric regulation theory based on the example of one of CGE models (CGE model of economic sectors) is shown. Optimal values of controlled parameters of economic politics are suggested based on the mathematical model examined. Dependencies of criterion optimal values on uncontrolled parameters for a given range of its values are found. The research results could be applied for the choice and realization of the effective budget and tax state policy.