On a Family of Volterra Cubic Stochastic Operators

In present paper we consider a family of discrete time Kolmogorov systems of three interaction population depending on a parameter $$\theta$$ . We show that there is the critic value $$\theta^{*}$$ of parameter $$\theta$$ such that for $$\theta\in(\theta^{*},1]$$ this evolution operator is a non-ergodic transformation and for $$\theta\in[0,\theta^{*})$$ it has property being regular. We give some biological interpretations of our results.

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