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  1. Mathematical Modeling of Biological and Social Evolutionary Macrotrends.Leonid Grinin, Alexander V. Markov & Andrey V. Korotayev - 2014 - In History & Mathematics: Trends and Cycles. Volgograd,Russia: Uchitel Publishing House. pp. 9-48.
    In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that the (...)
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  • A Mathematical Model of Juglar Cycles and the Current Global Crisis.Leonid Grinin, Andrey Korotayev & Sergey Malkov - 2010 - In Leonid Grinin, Peter Herrmann, Andrey Korotayev & Arno Tausch (eds.), History & Mathematics: Processes and Models of Global Dynamics.
    The article presents a verbal and mathematical model of medium-term business cycles (with a characteristic period of 7–11 years) known as Juglar cycles. The model takes into account a number of approaches to the analysis of such cycles; in the meantime it also takes into account some of the authors' own generalizations and additions that are important for understanding the internal logic of the cycle, its variability and its peculiarities in the present-time conditions. The authors argue that the most important (...)
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  • Early State and Democracy.Leonid Grinin - 2004 - In Leonid Grinin, Robert Carneiro, Dmitri Bondarenko, Nikolay Kradin & Andrey Korotayev (eds.), The Early State, Its Alternatives and Analogues. ‘Uchitel’ Publishing House. pp. 419--463.
    The present article is devoted to the problem which is debated actively to-day, namely whether Greek poleis and the Roman Republic were early states or they represented a specific type of stateless societies. In particular, Moshe Berent examines this problem by the example of Athens in his contribution to this volume. He arrives at the conclusion that Athens was a stateless society. However, I am of the opinion that this conclusion is wrong: and I believe that Athens and Rome were (...)
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  • History & Mathematics: Trends and Cycles.Leonid Grinin & Andrey V. Korotayev - 2014 - Volgograd: "Uchitel" Publishing House.
    The present yearbook (which is the fourth in the series) is subtitled Trends & Cycles. It is devoted to cyclical and trend dynamics in society and nature; special attention is paid to economic and demographic aspects, in particular to the mathematical modeling of the Malthusian and post-Malthusian traps' dynamics. An increasingly important role is played by new directions in historical research that study long-term dynamic processes and quantitative changes. This kind of history can hardly develop without the application of mathematical (...)
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  • Economic Cycles, Crises, and the Global Periphery.Leonid Grinin, Arno Tausch & Andrey Korotayev (eds.) - 2016 - Switzerland: Springer International Publishing Switzerland.
    This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifi cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfi lms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this (...)