论文标题
两位级系统中的进化行为
Evolutionary behavior in a two-locus system
论文作者
论文摘要
在此简短的说明中，我们研究了由两参数二次操作员生成的动力系统，将3维单纯形映射到本身。这是两个局部系统中配子频率的进化运算符。我们找到了所有（连续集）固定点的集合，并表明每个固定点都是非纤维的。我们完全描述了动态系统的所有极限点集。也就是说，对于任何初始点（取自3维单纯形），我们找到了一个不变的集合，其中包含算子的初始点和独特的固定点，因此初始点的轨迹会收敛到该固定点。
In this short note we study a dynamical system generated by a two-parametric quadratic operator mapping 3-dimensional simplex to itself. This is an evolution operator of the frequencies of gametes in a two-locus system. We find the set of all (a continuum set) fixed points and show that each fixed point is non-hyperbolic. We completely describe the set of all limit points of the dynamical system. Namely, for any initial point (taken from the 3-dimensional simplex) we find an invariant set containing the initial point and a unique fixed point of the operator, such that the trajectory of the initial point converges to this fixed point.
