The replication dynamics (differential equation system) is the foundation of evolutionary game theory. When n=2, there are four possible types of replication dynamics. When n=3, there are 49 possible types of replication dynamics. However, when n>3, the classification of replication dynamics has not been solved. In this article, the sufficient and necessary conditions of the replication dynamics equation with a unique fixed point in the interior of simplex $S_n$(Int$S_n$) for $n\geq 2$ are presented. Furthermore, the different types of replication dynamics equations with a unique fixed point in IntSn is discussed.

翻译：复制动力系统（微分方程组）是演化博弈论的基础。当n=2时，存在四种可能的复制动力系统类型。当n=3时，存在49种可能的复制动力系统类型。然而，当n>3时，复制动力系统的分类问题尚未解决。本文给出了当n≥2时，单形$S_n$内部(Int$S_n$)具有唯一不动点的复制动力系统方程的充分必要条件。此外，还讨论了IntSn中具有唯一不动点的不同复制动力系统方程的类型。