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Nonlinear Differential Equation of Macroeconomic Dynamics for Long-Term Forecasting of Economic Development

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Document pages: 24 pages

Abstract: In this article we derive a general differential equation that describeslong-term economic growth in terms of cyclical and trend components. Equationis based on the model of non-linear accelerator of induced investment. Ascheme is proposed for obtaining approximate solutions of nonlinear differentialequation by splitting solution into the rapidly oscillating businesscycles and slowly varying trend using Krylov-Bogoliubov-Mitropolsky averaging.Simplest modes of the economic system are described. Characteristicsof the bifurcation point are found and bifurcation phenomenon is interpretedas loss of stability making the economic system available to structural changeand accepting innovations. System being in a nonequilibrium state has a dynamicswith self-sustained undamped oscillations. The model is verified witheconomic development of the US during the fifth Kondratieff cycle(1982-2010). Model adequately describes real process of economic growth inboth quantitative and qualitative aspects. It is one of major results that themodel gives a rough estimation of critical points of system stability loss andfalling into a crisis recession. The model is used to forecast the macroeconomicdynamics of the US during the sixth Kondratieff cycle (2018-2050). Forthis forecast we use fixed production capital functional dependence on along-term Kondratieff cycle and medium-term Juglar and Kuznets cycles.More accurate estimations of the time of crisis and recession are based on themodel of accelerating log-periodic oscillations. The explosive growth of theprices of highly liquid commodities such as gold and oil is taken as real predictorsof the global financial crisis. The second wave of crisis is expected tocome in June 2011.

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