Asymptotical Behavior of Trajectories of Non-Volterra Quadratic Stochastic Operators

Аннотация

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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DOI

10.1134/s1995080222140165

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