具有比率依赖的HollingⅡ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 HollingⅡFunctional Response Fuction

作　　者：赵玉凤[1] ZHAO Yufeng(College of Computer and Information Engineering,Shanxi Technology and Business University,Taiyuan 030000,China)

机构地区：[1]山西工商学院计算机信息工程学院,山西太原030000

出　　处：《海南师范大学学报（自然科学版）》2024年第2期144-151,共8页Journal of Hainan Normal University（Natural Science）

基　　金：山西省高等学校科技创新项目(2022L645);山西省高等学校教学改革创新项目(J20221313);山西省教育科学“十四五”规划课题(GH-220495);山西工商学院教学改革创新项目(JG202043)。

摘　　要：研究了带有饱和发生率和比率依赖的HollingⅡ型功能反应函数的染病捕食者-食饵随机模型的动力学性质。首先构造合适的Lyapunov函数,利用Ito公式,通过反证法证明了在满足利普希茨条件下随机模型存在唯一的全局正解;然后,利用Ito公式、局部鞅的大数定律等随机微分方程的相关理论证明了系统在满足一定条件时食饵是持久的,易感捕食者和染病捕食者将逐渐灭绝;最后,通过数值仿真验证了结果的正确性,并得到了主要参数对模型的解产生的影响。In this paper,the dynamic properties of an infected predator-prey model with saturation incidence and ratio dependent HollingⅡfunctional 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 to the Ito formula and the method of proof to the contrary.Then,the relevant theories of stochastic differential equations such as Ito formulas and the law of large numbers for local martingales are used to prove that the prey is persistent,while susceptible and diseased predators will gradually become extinct when the system satisfies certain conditions.Finally,the correctness 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 HollingⅡ型功能反应函数 比率依赖 灭绝 

分 类 号：O175.12[理学—数学]