In this paper, we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure. Using the theory of generalized saddle-point behaviors, it is shown that there exists a [Formula: see text]-separatrix [Formula: see text] on its state space such that Species 2 wins the competition whenever the initial distribution is above [Formula: see text], while Species 1 wins the competition whenever the initial distribution is below [Formula: see text]. Combining with the previous conclusions of the system, we give a complete classification for global competitive dynamics. Furthermore, we carefully analyze the changes of the competition outcome after introducing the stage structure. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.

中文翻译：

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具有阶段结构的两物种竞争模型的双稳态

在本文中，我们关注具有阶段结构的两种 Lotka-Volterra 竞争模型的双稳态动态行为。使用广义鞍点行为理论，证明在其状态空间上存在一个[公式：见文本]-分隔线[公式：见文本]，使得物种 2 在初始分布高于 [公式：见正文]，而当初始分布低于 [公式：见正文] 时，物种 1 赢得比赛。结合前面系统的结论，我们对全球竞争动态给出了完整的分类。此外，我们在引入舞台结构后，仔细分析了比赛结果的变化。最后，提供了一些数值模拟来说明理论结果的有效性。