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The article deals with the global demographic transition and phenomenological models of demographic dynamics by Sergey Kapitsa and Boris Dolgonosov developed on the basis of the principles of demographic and informational imperatives. The technological imperative is analyzed, which is intermediate between the first two. The authors propose a new mathematical model for forecasting demographic dynamics in the era of widespread use of intelligent machines. The model has been developed on the basis of the demographic model of Sergey Kapitza and equations for the production of useful information in human society, based on the assumption of Sergey Kuznets about technological progress. Calculations made using this model show that the population of the Earth, having reached a maximum value c. 8.7 billion in 2060, will then begin to decline steadily and by 2100 will not exceed 8.3 billion.

The aim of this study was to develop an adequate mathematical model for long-term forecasting of technological progress and economic growth in the digital age (2020-2050). In addition, the task was to develop a model for forecast calculations of labor productivity in the symbiosis of “man + intelligent machine”, where an intelligent machine (IM) is understood as a computer or robot equipped with elements of artificial intelligence (AI), as well as in the digital economy as a whole. In the course of the study, it was shown that in order to implement its goals the Schumpeter-Kondratiev innovation and cycle theory on forming long waves (LW) of economic development influenced by a powerful cluster of economic technologies engendered by industrial revolutions is most appropriate for a long-term forecasting of technological progress and economic growth. The Solow neoclassical model of economic growth, synchronized with LW, gives the opportunity to forecast economic dynamics of technologically advanced countries with a greater precision up to 30 years, the time which correlates with the continuation of LW. In the information and digital age, the key role among the main factors of growth (capital, labour and technological progress) is played by the latter. The authors have developed an information model which allows for forecasting technological progress basing on growth rates of endogenous technological information in economics. The main regimes of producing technological information, corresponding to the eras of information and digital economies, are given in the article, as well as the Lagrangians that engender them. The model is verified on the example of the 5th information LW for the US economy (1982-2018) and it has had highly accurate approximation for both technological progress and economic growth. A number of new results were obtained using the developed information models for forecasting technological progress. The forecasting trajectory of economic growth of developed countries (on the example of the USA) on the upward stage of the 6th LW (2018-2042), engendered by the digital technologies of the 4th Industrial Revolution is given. It is also demonstrated that the symbiosis of human and intelligent machine (IM) is the driving force in the digital economy, where man plays the leading role organizing effective and efficient mutual work. Authors suggest a mathematical model for calculating labour productivity in the digital economy, where the symbiosis of “human + IM” is widely used. The calculations carried out with the help of the model show: 1) the symbiosis of “human + IM” from the very beginning lets to realize the possibilities of increasing work performance in the economy with the help of digital technologies; 2) the largest labour productivity is achieved in the symbiosis of “human + IM”, where man labour prevails, and the lowest labour productivity is seen where the largest part of the work is performed by IM; 3) developed countries may achieve labour productivity of 3% per year by the mid-2020s, which has all the chances to stay up to the 2040s.

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.

During the last millennium the world economic and geopolitical conflicts were to a great extent connected: different crises in the World System's evolution stimulated geopolitical shifts and vice versa. This article argues that in the 15th century different geopolitical events and conflicts in Central Asia initiated the fall of the previous World System and the rise of the new one. This transformation resulted in the fall of overland and river trade routes, including the Great Silk Route, which passed through Central Asia. World trade shifted to sea and ocean routes, and European countries became the center of the new World System. Now, in the beginning of the 21st century a new transformation of the World System is underway. The center of economic and political development is migrating gradually to the East: this is why the geopolitical role of the Central Asian states is increasing. Central Asian states are a very important part of the New Silk Route; this route is to connect Eastern Asia with Europe an...

There are grounds to conclude that in 2011–2012 the World System experienced to some extent a phase transition to a qualitatively new state of global protest activity. This phase transition is shown to bear some resemblance to the one which the World System experienced in the early 1960s. The first (after 1919) phase transition of this sort occurred in the early 1960s and was related to the growth of global informational connectivity after World War II, as well as the improvement of the means of protest self-organization due to the spread of television, portable radio receivers, portable electric loud-speakers and other technologies of the Fourth Kondratieff Cycle. The phase transition of the early 2010s was prepared by a new wave of growth of global informational connectivity, as well as the improvement of the means of protest self-organization due to the spread of various technologies of the Fifth Kondratieff cycle (the Internet, satellite television, Twitter and other social networks, mobile telephony etc.). Similarly to what was observed during the Fourth Kondratieff Wave, during the Fifth Cycle while the spread of these technologies was going on for many years before 2011, their internal colossal potential for generating and spreading protest activity was realized in one leap, as a phase transition.

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

How are large technological changes and important shifts in international politics interconnected? It is shown in the article that primary technological innovations, which take place in each Kondratieff cycle, change the balance of power between the leading states and cause shifts in international politics. In the beginning of the twenty-first century, the genesis and initial development of the cluster of new technologies takes place in periods of crisis and depression. Therefore, the authors forecast that the period 2013–2020 will be marked by the advancement of important technological innovations and massive geopolitical shifts in many regions of the world.

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.

This article continues our analysis of the gold price dynamics that was published in December 2010 and forecasted the possibility of the “burst of the gold bubble” in April –June 2011. Our recent analysis suggests the possibility of one more substantial fluctuation before the final collapse in July 2011. On the other hand, in early 2011 we detected a number of other commodity bubbles and forecasted the start of their collapse in May – June 2011. We demonstrate that this collapse has actually begun, which in conjunction with the forthcoming burst of the gold bubble suggests that the World System is entering a bifurcation zone bearing rather high risks of the second wave of the global financial-economic crisis.

The analysis of the gold price series for 2003–2010 employing both the methodology developed by Didier Sornette and the one of the authors allows forecasting the collapse in gold prices in April – June 2011. The article discusses both the scenarios that could allow avoiding this collapse, and the possibilities of the “gold bubble burst” leading to the second wave of the global economic crisis.