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In this article we derive a general differential equation that describes long-term economic growth in terms of cyclical and trend components. Equation is based on the model of non-linear accelerator of induced investment. A scheme is proposed for obtaining approximate solutions of nonlinear differential equation by splitting solution into the rapidly oscillating business cycles and slowly varying trend using Krylov-Bogoliubov-Mitropolsky averaging. Simplest modes of the economic system are described. Characteristics of the bifurcation point are found and bifurcation phenomenon is interpreted as loss of stability making the economic system available to structural change and accepting innovations. System being in a nonequilibrium state has a dynamics with self-sustained undamped oscillations. The model is verified with economic development of the US during the fifth Kondratieff cycle (1982-2010). Model adequately describes real process of economic growth in both quantitative and qualitative aspects. It is one of major results that the model gives a rough estimation of critical points of system stability loss and falling into a crisis recession. The model is used to forecast the macroeconomic dynamics of the US during the sixth Kondratieff cycle (2018-2050). For this forecast we use fixed production capital functional dependence on a long-term Kondratieff cycle and medium-term Juglar and Kuznets cycles. More accurate estimations of the time of crisis and recession are based on the model of accelerating log-periodic oscillations. The explosive growth of the prices of highly liquid commodities such as gold and oil is taken as real predictors of the global financial crisis. The second wave of crisis is expected to come in June 2011.

The paper analyzes the current state of the world economy and offers a short-term forecast of its development. Our analysis of log-periodic oscillations in the DJIA dynamics suggests that in the second half of 2017 the United States and other more developed countries could experience a new recession, due to the third phase of the global financial crisis. The economies of developing countries will continue their slowdown due to lower prices of raw commodities and the increased pressure of dollar debt load. The bottom of the slowdown in global economic growth is likely to be achieved in 2017-2018. Then we expect the start of a new acceleration of global economic growth at the upswing phase of the 6th Kondratieff cycle (2018-2050). A speedy and steady withdrawal from the third phase of the global financial crisis requires cooperative action between developed and developing countries within G20 to stimulate global demand, world trade and a fair solution of the debt problem of developing countries., Comment: 34 pages, 10 figures

The analysis of dollar inflation performed by the authors through the approximation of empirical data for 1913–2012 with a power-law function with an accelerating log-periodic oscillation superimposed over it has made it possible to detect a quasi-singularity point around the 17th of December, 2012. It is demonstrated that, if adequate measures are not taken, one may expect a surge of inflation around the end of this year that may also mark the start of stagflation as there are no sufficient grounds to expect the re-start of the dynamic growth of the world economy by that time. On the other hand, as the experience of the 1970s and the 1980s indicates, the stagflation consequences can only be eliminated with great difficulties and at a rather high cost, because the combination of low levels of economic growth and employment with high inflation leads to a sharp decline in consumption, aggravating the economic depression. In order to mitigate the inflationary consequences of the explosive growth of money (and, first of all, US dollar) supply it is necessary to take urgently the world monetary emission under control. This issue should become central at the forthcoming G8 and G20 summits.