A Mathematical Model of Juglar Cycles and the Current Global Crisis
Though the issue of economic cycles has been subject to numerous studies, this problem has retained its high importance. What is more, the current crisis has confirmed in an extremely convincing way the point that, notwithstanding all the successes achieved by many states in their countercyclical policies, no economy is guaranteed against uncontrollable upswings and unexpected crises and recessions that tend to follow such upswings. In addition to this, the financial globalization has increased substantially the risks of such cyclical fluctuations.
The notion of economic cycles is regarded ambiguously in economic science. In modern theories, business cycles are frequently defined as fluctuations of actual output around its potential value which is achieved in full employment conditions (see, e.g., Fischer, Dornbusch, and Schmalensee 1988). However, quite frequently economics does not achieve on the rise the potential GDP volume when a recession phase starts (such situations are described in more detail in Гринин, Коротаев 2009а: ch. 1). Thus, economic cycle, in our opinion, can be defined as periodical fluctuation around medium line of production volume, where repeating phases of rise and decrease can be specified.
In the model that we propose below we have tried to briefly describe
the main features of medium-term cycles of business activity, or business cycles (7–11 years) that are also known as Juglar cycles after the prominent
19th-century French economist Clement Juglar (1819–1905), who investigated these cycles in detail (Juglar 1862, 1889).
 Many economists maintain that business cycles are quite regular with the characteristic period of 7–11 years. However, some suggest that economic cycles are irregular (see, for example, Fischer, Dornbusch, and Schmalensee 1988). As we suppose, comparative regularity of business cycles is observed rather at the World System scale than in every country taken separately. This
corroborates the important role of exogenous factors for the rise and progress of business cycles (for more detail see below).
 Medium-term cycles (7–11 years) were first named after Juglar in works by Joseph Schumpeter, who developed the typology of different-length business-cycles (Schumpeter 1939, 1954; see also Kwasnisсki 2008).