Korotayev A., Malkov A., Khaltourina D. Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends. Moscow: URSS, 2006. 176 pp. OTHER BOOKS BY THESE AUTHORS: History and mathematics: Analyzing and Modeling Global Development History and mathematics: Historical Dynamics and Development of Complex Societies. Hierarchy and Power in the History of Civilizations: Ancient and Medieval Cultures. Hierarchy and Power in the History of Civilizations: Political Aspects of Modernity. The Early State, Its Alternatives and Analogues. Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends in Africa. We also recommend "Social Evolution & History". International journal published since 2002.     Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth at Google Books Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends.

Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth at Google Books

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Korotayev, A., A. Malkov, and D. Khaltourina. Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends. Moscow: KomKniga/URSS, 2006. P. 37–46.

Chapter 1

Secular Cycles

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We believe that one of the most important recent findings in the study of the long-term dynamic social processes was the discovery of the political-demo­graphic cycles as a basic feature of complex agrarian systems' dynamics.[1]

The presence of political-demographic cycles in the pre-modern history of Europe and China has been known for quite a long time (e.g., Postan 1950, 1973; Abel 1974, 1980; Le Roy Ladurie 1974; Hodder 1978; Braudel 1973; Chao 1986; Cameron 1989; Goldstone 1991; Kul'pin 1990; Mugruzin 1986, 1994 etc.), and already in the 1980s more or less developed mathematical models of demographic cycles started to be produced (first of all for Chinese "dynastic cycles") (Usher 1989). At the moment we have a very considerable number of such models (Chu and Lee 1994; Nefedov 1999e, 2002a; 2004; S. Malkov, Kovalev, and A. Malkov 2000; S. Malkov and A. Malkov 2000; Malkov and Sergeev 2002, 2004a, 2004b; Malkov et al. 2002; Malkov 2002, 2003, 2004; Turchin 2003, 2005a).[2]

               Recently the most important contributions to the development of the mathematical models of demographic cycles have been made by Sergey Nefedov, Peter Turchin and Sergey Malkov. What is important is that on the basis of their models Nefedov, Turchin and Malkov have managed to demonstrate that demographic cycles were a basic feature of complex agrarian systems (and not a specifically Chinese, or European phenomenon).

Nefedov (2004) starts with the population model developed by Raymond Pearl (1926) and described by the logistic equation suggested by Verhulst (Verhulst 1838; see also, e.g., Riznichenko 2002; Korotayev, Malkov, and Khaltourina 2006):

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