Abstract In the present paper we consider a family of non-Volterra quadratic stochastic operators depending on a parameter α and study their trajectory behaviors. We find all fixed and periodic points for a non-Volterra quadratic stochastic operator on a finite-dimensional simplex. A complete description of the set of limit points is given, and we show that such operators have the ergodic property.

中文翻译：

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对应于排列的二次运算符

摘要 在本文中，我们考虑了一系列依赖于参数 α 的非 Volterra 二次随机算子并研究了它们的轨迹行为。我们在有限维单纯形上找到非 Volterra 二次随机算子的所有不动点和周期点。给出了极限点集的完整描述，并且我们证明了这样的算子具有遍历性质。