Department of Mathematics, Taiyuan University of Technology, Taiyuan, People's Republic of China.
J Biol Dyn. 2024 Dec;18(1):2366495. doi: 10.1080/17513758.2024.2366495. Epub 2024 Jun 20.
In this paper, we consider a stochastic two-species predator-prey system with modified Leslie-Gower. Meanwhile, we assume that hunting cooperation occurs in the predators. By using Itô formula and constructing a proper Lyapunov function, we first show that there is a unique global positive solution for any given positive initial value. Furthermore, based on Chebyshev inequality, the stochastic ultimate boundedness and stochastic permanence are discussed. Then, under some conditions, we prove the persistence in mean and extinction of system. Finally, we verify our results by numerical simulations.
在本文中，我们考虑了一个具有修正 Leslie-Gower 的随机双种群捕食者-被捕食者系统。同时，我们假设捕食者之间存在合作捕食。通过使用 Ito 公式和构造适当的 Lyapunov 函数，我们首先证明了对于任意给定的正初始值，系统存在唯一的全局正解。此外，基于切比雪夫不等式，讨论了随机有界和随机持久性。然后，在一些条件下，我们证明了系统的均值持续和灭绝。最后，通过数值模拟验证了我们的结果。
