A. S. Mulkidjan

The article is devoted to the research of the models of economic processes with fluctuations, relevant to the growth and recession of the economy. It is known that the models of this type are essentially non-linear, the presence of limitations and assumptions about the leaps are typical for them. In this situations may appear the conditions, leading to the re-gularization. The assumption that anytime t economy has fixed capital K, the volume of which varies with speed , rational to net investments and the total wear during the concerned period, is used. The case of linear dependence between production volume Y and consumption X is studied. It is shown that periodic behavior of Y and K quantities may arise as a consequence of oscillations in the investment. The economic cycle for the model with extreme investment policy is considered, a graphical representation of the economy state in the phase plane is given. The phase portrait of economy model with fluctuations is built. Basic relationships between the variables of economic model with fluctuations are determined. Model equation is transformed into the of Rayleigh type equation, for which a stable limit cycle exists. The origin conditions of limit cycles are studied. The possibility of applying of the indexed-divergence method for the studying of the stability of solutions of the model equations is considered. Models with fluctuations describe a wide class of dynamic processes of the economy, that allows to apply these models and the results of their research for the development of the methods and technologies of industrial business control.