Utkir Rozikov
dates de séjour
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projet de recherche
Non-linear Dynamical Systems: Evolution of Sex-linked Populations and Thermodynamics of Spin Systems Related to the Physics on Graphs
The project has two directions: A) The first direction will be devoted to dynamical systems, social networks, disease propagation in populations and evolution algebras (genetic, algebras of free and bisexual population etc.) and their applications to population biology. We will study non-archimedean (p-adic) analogies of the biological systems and apply the results to the theory of cataclysm (catastrophe). B) The project is also aimed at studying the thermodynamics (in physics and biology) and pure phases (extreme Gibbs measures) of several spin systems on graphs. We will also apply the theory of Gibbs measures to the fields of neural and communication networks. Moreover, we will study phase transition problems of spin systems over the field of p-adic numbers.
biographie
Utkir Rozikov is a Professor at the Institute of Mathematics in the Department of Algebra and Analysis, in Tashkent University (Uzbekistan). He graduated from the Faculty of Mathematics and Mechanics of Samarkand State University in 1993, and defended his Ph. D. thesis in 1995. His D. Sci. thesis was defended in 2001. His research interests include: dynamical systems, trajectory theory of dinamical systems, nonlinear operators and processes, random walks in random environment, p-adic analysis, the Gibbs measures, lattice models of statistical mechanics, quadratic stochastic operators, simplex, trajectory, Volterra and non-Volterra stochastic operators.
