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Functional analysis and its applications
February 16, 2023 08:30–09:30
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Dissertation discussion
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Quadratic stochastic dynamical systems of the type $(\sigma |\mu)$ (PhD dissertation discussion)
S. S. Khudayarov Bukhara State University
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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
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