Analysis of the features of economic systems with a small parameter

The relevance of this study is obvious. The rapid rise in inflation, fueled by a significant increase in wages in some sectors of the economy, and inflationary expectations are making life very difficult for society as a whole. The goal is to determine the level of GDP that will ensure stability in the country's economy and in the lives of its citizens for a long time. The article presents a study of the macroeconomic model of the Goodwin business cycle, which includes a small parameter in order to predict the dynamics of changes in vital economic indicators. For its analysis, such a method of dynamical systems theory as the method of normal forms by A. Poincare was used. It is shown that such a model can have a stable cycle in the vicinity of the state of economic equilibrium. Asymptotic formulas for calculating periodic solutions are obtained. The quantitative size of the limit cycle has been determined, which reflects periodic processes occurring in the economic system Goodwin, according to the input parameters. The stability of these processes has been proven. The results of the study clearly illustrate that the desired sustainable cyclical pattern of economic development, which allows the state to develop effectively, does not occur in all cases. In addition, it is also quite difficult to draw conclusions about the scope of this cycle from a practical point of view. But if it succeeds, then it is possible to make long-term forecasts regarding the development and the level of the main economic indicators that this development will ensure.

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