#### For citation:

Kurkina E. S., Knjazeva E. N. Sergey P. Kurdyumov and his evolutionary model of dynamics of complex systems. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2013, vol. 21, iss. 4, pp. 135-217. DOI: 10.18500/0869-6632-2013-21-4-135-217

# Sergey P. Kurdyumov and his evolutionary model of dynamics of complex systems

Sergei P. Kurdyumov (1928–2004) and his distinguished contribution in the development of the modern interdisciplinary theory and methodology of study of complex selforganizing systems, i.e. synergetics, is under consideration in the article. The matter of a mathematical model of evolutionary dynamics of complex systems elaborated by him is demonstrated. The nonlinear equation of heat conductivity serves as a basis of the model. Under certain conditions, it describes dynamics of development of structures of different complexity in the blow-up regime. Methods of calculation of two-dimentional structures which are described by automodel solutions are considered; and their classification is given. The automodel problem is a boundary problem aiming to find eigen-values and eigen-functions for a nonlinear equation of elliptical type on a plane. Proceeding from the analysis of the model, a principle of coevolution was formulated by S.P. Kurdyumov. This is the principle of integration of simple structures into a complex one. Three notions of great significance follow from the principle, and namely: the notion of connection of space and time, the notion of complexity and its nature and the notion evolutionary cycles and switching over different regimes as a necessary mechanism of maintenance of «life» of complex structures. Approaches of possible application of this model for understanding of dynamics of complex social, demographic and geopolitical systems are viewed as well.

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