Stochastic modeling of complex systems

Y. Kondratiev


The  aim  of  this  short  note  is  to  give  a  brief  description  (oriented  on non-mathematical audience) concerning some directions under an active development in the theory of complexity which are closely related to the scientific activity of the Interdisciplinary Research Center for Complex Systems (IRCCS) at the Dragomanov National Pedagogical University. This review is based on the talk given at the First annual meeting of IRCCS in September 2012. We will try to present certain key ideas in the area without an attempt to give an overview complete at any extend. It is why the references are restricted to minima just to give, for the motivated reader, some sources of a more detailed explanation. This note may be considered as an introduction into the more mathematical description of the corresponding problems of stochastic dynamics for complex systems which is presented in the next article of the present journal issue.

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Ph. Ball, Critical Mass: How One Thing Leads to Another, London: Heine- mann, 2004

G. Giacomin, J. Lebowitz, E. Presutti, Deterministic and stochastic hydrodynamic equations arising in from simple microscopic model systems, Math. Surveys AMS (Volume 64), 107–149, 1999

D. Finkelshtein, Yu. Kondratiev, O.Kutoviy, Individual based models with competition in spatial ecology, SIAM J. Math. Anal. (Volume 41) 297–317, 2009

D. Finkelshtein, Yu. Kondratiev and O. Kutoviy, Vlasov scaling for stochastic dynamics of continuous systems, J. Stat. Phys. (Volume 141), 158–178, 2010

D. Finkelshtein, Yu. Kondratiev and O. Kutoviy, Semigroup approach to non-equilibrium birth-and-death stochastic dynamics in continuum, J. Funct. Anal. (Volume 262) 1274–1308, 2012

S. A. Levin, Complex adaptive systems: Exploring the known, the unknown and the unknowable, Bull. Amer. Math. Soc., (Volume40), 3–19, 2002

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