A.A.Ashimov, M.A.Beisenbi.

The Republic of Kazakhstan. Almaty.

The institute of information and management problems of MES RK.

E-mail: LNS @ ipis.academ.Alma-Ata.su.


Abstract. Offered mathematical model macroeconomical and information system of a simulation modeling, values other scenario of development of economy of country.


А.А. Ашимов, М.А. Бейсенби.

Республика Казахстан, г. Алматы.

Институт проблем информатики и управления МОН РК.

E-mail: LNS @ ipis.academ.Alma-Ata.su.


Аннотация. Предлагается макроэкономическая математическая модель и информационная система имитационного моделирования, позволяющая оценить разные сценарии развития экономики страны.


Economic life of sufficiently far off complex of society, which possible definitely confirms that any staff an working perspective economic program or public-economic reform require serious scientific occupations. Economic system does not allow product and enterprise target-oriented experiments natural required for deep and detailed analysis of development of economy of country. Ithaca, impossible exactly and cheque public-economic politician generally accepted in natural sciences by fetters, on which experiment with the nature.

On the light has said an object or ambience of experiment can be only images real economy models; modeling models is experimented in the computer - the most natural system economic analysis facility. If manage to build sufficiently identical mathematical model, modeling is experimented on her by means of the computer to gain a feature of full-fledged scientific analysis and allows on the lecturer of complex of output factors (pointers) value other scenario of development of economy of country depending on economic, public, budgetary and politicians conditions.

Important place is conducted here questions of evaluation of efficiency [1] financial-credit, investment politicians and foreign economic state activity. So-so important and actual development of mathematical models [2], acceptable describing total principles and regularities of economic process development in the system, so it it is necessary does technologies information and system of modeling of modeling, intended for the support of deciding central tel of control be pointed to macroeconomical in the regulation within the framework of shaping a professional government.

In the given operation with provision for modern conditions of methods of system analysis of economic system development is designed dinamical mathematical model and system of modeling of modeling information, stability of value, stability and forecasting prospects of development of economy of country. In the economic model system presents in the lecturer as a collection acting agents, for which clamped defining economic functions. Agents - product, population, bank system, condition, market of labour, goods and money.

Economic country development in the system information is evaluated: price level and inflation, nominal value and real VVP , number unemployed in the country, postpones an economy an monetization, forms an arrival amount tax in the budget of state, credit rate level and etc.

Simulation modeling is realized in the ambience VISIAL FOXPRO-5.0., guaranteeing the most broad object-oriented programming possibilities.

Information system of a simulation modeling allows to track other scenario of development of economy of country under other contribution of combinations (initial) data and mechanisms of macroeconomical government regulation.

The numeric experiment in the simulation system allows:

- to value an influence of financial emission and including a money a development of economy of country;

- to value an influence of credit and investment politicians be referenced in the economic system development;

- to value politicians of tax of influence of condition in the economic system development;

- to value an influence public politicians of condition in the economic system development;

- to forecast structures of lecturer of population, toil a facility and unemployed in the country;

- to value an influence of expenseses of condition in protection, formation, science, contents of the state basis and ò. ä., in public-economic country development;

-to forecast arrivals in the budget of condition and etc.

On mathematical model of economic system is showed the diversity of types of price levels on goods market, which varies from simple equilibrium points to plural periodic or chaotic attractors.

In development of economics in deferent countries are known the periods of erases, during which market mechanisms became unstable. Unstabilities of market mechanisms are directly determined by conducted monetary, fiscal, investment policies and external economic activity of state. Their strike scientific analysis should be based on accurate mathematical description of process of functioning of economic system in whole. Possibility of research on mathematical models of conditions of loosing stability of equilibrium conditions of market mechanisms appeaved thanks to development of theory of open non-linear dynamic systems with managing and/or disturbing influences in shape of exchange of energy, substance and information.

In resent years was received a number of important results such as strange attractors (D.Ruel, F.Takens 1971),chaos in determinist systems (T.Lee, D.Yorhe,1975) Feigenbaum¢ s universalism (M.J. Feigenbaum, 1978), was developed a qualitative theory of dynamic systems (R.Thom, A.Arnold and others) and theory of selg-organisation (H.Prigojin, C.Nicolis, Haken and others), where is mathematically based and showed on the example of processes in physics, chemistry and biology an outcome in non-linear dynamic systems complex behavior.

Research of price level stability on the commodity market is based on single measured points reflection methods. For this the model of economic system in continuos time, is carried to model with discrete time determined only by recurrent correlation with relation of price levels on the commodity market.

It is showed that given discrete reflection corresponds to infinite sequma of bifurcation under certain values of parameters each of them brings to stable cycles of higher sequence with period doubling under every consequent bifurcation, turning into conditions with brightly expressed chaotic behavior.

Regularities of a dynamic approach of price of price levels on the market to sphere of chaotic behavior (strange attractor) are coordinated with results of Fiegenbaum’s universalism law. Parameters of bifurcation are directly determined by rate of economic growth, deprecation of basic fund, money growth, credits, export and import volume, initial values of basic funds volume and money in economic, etc.

There is proposed an approach to an election of function of surplus demand and supply from class of structure-sable reflections, which allows maximum increase sphere of robust stability of equilibrium trajectories of economic system development, that is allowing asymptotic stability of equilibrium price levels on goods market at any change of uncertain and regulated parameters of economic system.


1. R Kempbell., Makkonell, Shaving Stenly L.. Economics: Principles, problems and policy. In 2-h volumes: Translation with english т. 1,2., Tallin, 1993.

2. Petrov А.А., Pospelov I.G, Shananin А.А. Experience of mathematical modeling of economy. М.: Energoatomizdat, 1996. - 544 With.

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