Asymptotical Behavior of Trajectories of Non-Volterra Quadratic Stochastic Operators
Uygun JamilovRomanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, 100174, Tashkent, UzbekistanB. J. MamurovBukhara State University, Faculty of Physiscs and Mathematics, 705018, Bukhara, Uzbekistan
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Annotatsiya
In the paper, we consider a family of discrete-time dynamical systems generated by non-Volterra stochastic operators. Namely non-Volterra stochastic operators depending on the two parameters $$a,b\in[-1,1]$$ . It is described the set of fixed points and their types and the set of periodic points. We proved that for any parameters any trajectory of a non-Volterra QSO from this family converges to either period point with period two or a fixed point, that is we showed that such operators have a property of being ergodic.
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