In the present paper, we consider non-Volterra cubic stochastic operators defined on a finite-dimensional simplex depending on a permutation π and a parameter α. We showed that for any permutation π, except the identity permutation, the set of limit points of the trajectories corresponding to the operators converges to a periodic trajectory. The trajectories of the operator corresponding to the identity permutation converge to a fixed point.

中文翻译：

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（π，α）-三次随机算子的动力学

在本文中，我们考虑了根据置换π和参数α在有限维单纯形上定义的非Volterra三次随机算子。我们表明，对于任何置换π，除了身份置换，对应于算子的轨迹的极限点集都收敛到周期轨迹。与身份置换相对应的算子的轨迹收敛到固定点。