Abstract

In the present paper, we study dynamical systems generated by stochastic operators which are superpositions of extremal Volterra and non-Volterra quadratic stochastic operators defined on the two-dimensional simplex. It is described the set of all periodic and the set of all fixed points of such operators. Further for such operator we showed that for an initial point their trajectory either converges to a periodic trajectory or diverges.

中文翻译：

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关于 Volterra 和置换 Volterra 二次随机算子的叠加

 抽象的

在本文中，我们研究由随机算子生成的动力系统，这些随机算子是在二维单纯形上定义的极值 Volterra 和非 Volterra 二次随机算子的叠加。描述了此类算子的所有周期的集合和所有不动点的集合。对于这样的算子，我们进一步表明，对于初始点，它们的轨迹要么收敛到周期性轨迹，要么发散。