V.V. Andreev, M.I. Semenov

The important place at acceptance of administrative decisions occupies ability to expect possible ways of development of the various processes proceeding in socially - economic system. The mathematical model of social and economic system on the basis of principles «predator-victim» is developed. As the basic co-operating elements of model characterising the social and economic system, are chosen: budget incomes; a total internal product (gross national product); expenses on science financing; population incomes; a budgeted deficit. The mathematical model is applied to the analysis and situation forecasting in the USA. Optimum parametrical identification of model with the real data of the state statistics was made on the basis of Levenberg- Marquardt algorithm in Fletcher's updating. In comparison with standard methods this algorithm yields the best results for the decision of the redefined nonlinear equations systems. Results of research have shown that at preservation of current trends in economy, second half of 2010 and 2011 years will be very heavy for the USA. At the same time it is necessary to notice that the investigated model defines tendencies of dynamics of socially - economic system. In time the made effective administrative decisions will help to pass crisis stages of development with the minimum losses.