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Modeling general laws of spatial–temporal evolution of society: hyperbolic growth and historical cycles

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The article investigates a distributed model of global evolution of humanity. The model utilizes a onedimensional quasilinear heat equation with a volume source and a nonlinear thermal conductivity coefficient. The model is applied to describe cyclic processes that unfolded over the entire span of human evolution against the backdrop of general population growth with blowup. The model parameters are chosen so that they satisfy the following requirements: the space integral (total population size) increases hyperbolically; the evolution of the system goes through 11 stages corresponding to the main historical epochs in accepted classification and matches actual quantitative indicators.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    E. D. Kuretova & E. S. Kurkina

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  1. E. D. Kuretova
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  2. E. S. Kurkina
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Correspondence to E. D. Kuretova.

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Translated from Prikladnaya Matematika i Informatika, No. 32, pp. 67–96, 2009.

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Kuretova, E.D., Kurkina, E.S. Modeling general laws of spatial–temporal evolution of society: hyperbolic growth and historical cycles. Comput Math Model 21, 70–89 (2010). https://doi.org/10.1007/s10598-010-9055-9

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