海南师范大学学报（自然科学版）2024，Vol.37Issue(2)：144-151,8.DOI:10.12051/j.issn.1674-4942.2024.02.002
具有比率依赖的Holling Ⅱ型功能反应函数的染病捕食者-食饵随机模型的动力学分析
Dynamical Analysis of an Infected Predator-prey Stochastic Model with Ratio-dependent Holling Ⅱ Functional Response Fuction
摘要
Abstract
In this paper,the dynamic properties of an infected predator-prey model with saturation incidence and ratio de-pendent Holling Ⅱ functional response function are studied.Firstly,a suitable Lyapunov function is constructed.It is proved that there exists an unique global positive solution for the stochastic model under the Lipschitz condition by using the Itô formula and the method of proof to the contrary.Then,the relevant theories of stochastic differential equations such as Itô formulas and the law of large numbers for local martingales are used to prove that the prey is persistent,while suscep-tible and diseased predators will gradually become extinct when the system satisfies certain conditions.Finally,the correct-ness of the results are verified by numerical simulation,and the influence of the main parameters on the solutions of the model are obtained.关键词
染病捕食者-食饵随机模型/饱和发生率/Holling Ⅱ型功能反应函数/比率依赖/灭绝Key words
infected predator-prey stochastic model/saturation incidence/Holling Ⅱ functional response function/ratio-dependent/extinction分类
数理科学引用本文复制引用
赵玉凤..具有比率依赖的Holling Ⅱ型功能反应函数的染病捕食者-食饵随机模型的动力学分析[J].海南师范大学学报（自然科学版）,2024,37(2):144-151,8.基金项目
山西省高等学校科技创新项目(2022L645) （2022L645）
山西省高等学校教学改革创新项目(J20221313) （J20221313）
山西省教育科学"十四五"规划课题(GH-220495) （GH-220495）
山西工商学院教学改革创新项目(JG202043) （JG202043）
