Seminars: S. S. Khudayarov, Quadratic stochastic dynamical systems of the type $(\sigma |\mu)$

SEMINARS


Seminar on Modern Problems of Complex Analysis (Sadullaev Seminar) February 16, 2023 11:30, Tashkent, National University of Uzbekistan, Room A304 (Department of Mathematics)

Quadratic stochastic dynamical systems of the type $(\sigma \|\mu)$ S. S. Khudayarov Bukhara State University
Abstract: The thesis is devoted to investigation of the dynamical systems generated by stochastic and non-stochastic cubic matrices. Basic results of the research are as follows: Necessary and sufficient conditions to coefficients of the of quadratic operator to map the simplex ${{S}^{m-1}}$ to itself are found. All fixed points of discrete and continuous-time quadratic stochastic and non-stochastic operators defined in the simplex were found and the limit points of the trajectory were studied. The dynamics of a one-dimensional quadratic non-stochastic operator is studied in general. Conditions for the parameters of the one-dimensional quadratic nonstochastic operator to form a chaotic dynamical system are given. For a class of two-dimensional quadratic non-stochastic operators it is shown that among two-dimensional quadratic non-stochastic operators in particular, there are those that form a chaotic dynamical system and those that do not form a chaotic dynamical system. Some multiplication operations for cubic matrices are introduced, and a family of matrices satisfying the Kolmogorov-Chapman equation for these multiplications is determined. Several examples of quadratic stochastic processes of type $(\sigma \|D)$ have been constructed. Website: https://us02web.zoom.us/j/8022228888?pwd=b3M4cFJxUHFnZnpuU3kyWW8vNzg0QT09