具有阶段结构和Allee效应的捕食–食饵模型的随机动力学分析  

Stochastic Dynamics Analysis of a Predator-Prey Model with Stage Structure and Allee Effect

作　　者：冯赛提 张天四[1] 

机构地区：[1]上海理工大学理学院,上海

出　　处：《应用数学进展》2021年第4期909-922,共14页Advances in Applied Mathematics

摘　　要：本文研究了一类具有阶段结构和Allee效应的捕食–食饵模型的随机动力学行为。首先,我们讨论的模型是由3个随机微分方程构成,它主要描述了食饵、未成熟捕食者和成熟捕食者之间的相互作用。其次,为了证明模型存在全局唯一正解,我们构造多个合适的李雅普诺夫函数,并建立了系统存在遍历平稳分布的条件。最后,我们建立了食饵和两个捕食者灭绝的条件。In this paper, the stochastic dynamics of a predator-prey model with stage structure and Allee effect is handled and established based on some suitable Lyapunov functions. First of all, our model is composed of three random differential equations, which describes the interaction between predator species and prey. Secondly, to prove the existence of a globally unique positive solution to the model, we construct several appropriate Lyapunov functions, and then establish the conditions for the existence of ergodic stationary distribution for the system. Finally, we establish the extinction conditions for the prey and two species of predator.

关 键 词：捕食–食饵模型 ALLEE效应 随机 阶段结构 平稳分布 灭绝 

分 类 号：O17[理学—数学]