In the present paper, we consider a convex combination of non-Volterra quadratic stochastic operators defined on a finite-dimensional simplex depending on a parameter \(\alpha \) and study their trajectory behaviours. We showed that for any \(\alpha \in [0,1)\) the trajectories of such operator converge to a fixed point. For \(\alpha =1\) any trajectory of the operator converges to a periodic trajectory.

中文翻译：

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关于作用于单纯形的非Volterra型二次算子族

在本文中，我们考虑了根据参数\（\ alpha \）在有限维单纯形上定义的非Volterra型二次随机算子的凸组合，并研究了它们的轨迹行为。我们表明，对于任何\（\ [0,1）中的alpha），此类算子的轨迹都收敛到固定点。对于\（\ alpha = 1 \），算子的任何轨迹都收敛到周期性轨迹。