Abstract In the present paper, we focus on a stochastic predator-prey model with stage structure for prey. Firstly, by using the stochastic Lyapunov function method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases. Some examples and numerical simulations are carried out to validate our analytical findings.

中文翻译：

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具有猎物阶段结构的随机捕食者-猎物模型的动力学行为

摘要 在本文中，我们关注具有猎物阶段结构的随机捕食者-猎物模型。首先，通过使用随机Lyapunov函数方法，我们得到了模型正解的遍历平稳分布存在唯一性的充分条件。然后我们在两种情况下建立捕食者种群灭绝的充分条件。进行了一些示例和数值模拟以验证我们的分析结果。