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Contemporary theories 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 the dynamics of complex agrarian systems. The presence of political-demographic cycles in the pre-modern history of Europe and China, and in chiefdom level societies worldwide has been known for quite a long time,[3] 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 1999, 2002, 2003, 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; Korotayev et al. 2006). Recently the most important contributions to the development of the mathematical models of long-term ("secular") sociodemographic cycles have been made by Sergey Nefedov, Peter Turchin, Andrey Korotayev, and Sergey Malkov.[4] What is important is that on the basis of their models Nefedov, Turchin and Malkov have managed to demonstrate that sociodemographic cycles were a basic feature of complex agrarian systems (and not a specifically Chinese or European phenomenon). The basic logic of these models is as follows: After the population reaches the ceiling of the carrying capacity of land, its growth rate declines toward near-zero values. The system experiences significant stress with decline in the living standards of the common population, increasing the severity of famines, growing rebellions etc. As has been shown by Nefedov, most complex agrarian systems had considerable reserves for stability, however, within 50–150 years these reserves were usually exhausted and the system experienced a demographic collapse (a Malthusian catastrophe), when increasingly severe famines, epidemics, increasing internal warfare and other disasters led to a considerable decline of population. As a result of this collapse, free resources became available, per capita production and consumption considerably increased, the population growth resumed and a new sociodemographic cycle started. It has become possible to model these dynamics mathematically in a rather effective way. Note that the modern theories of political-demographic cycles do not deny the presence of trend dynamics and attempt at the study of the interaction between cyclical and trend components of historical dynamics. Modern social scientists from different fields have introduced cycle theories to predict civilizational collapses in approaches that apply contemporary methods that update the approach of Spengler, such as the work of Joseph Tainter suggesting a civilizational life-cycle. In more micro-studies that follow the work of Malthus, scholars such as David Lempert have presented "alpha-helix" models of population, economics, and political response, including violence, in cyclical forms that add aspects of culture change into the model. Lempert has also modeled political violence in Russian society, suggesting that theories attributing violence in Russia to ideologies are less useful than cyclical models of population and economic productivity.