一类随机捕食系统的平稳分布及其概率密度函数  

Stationary distribution and probability density function of a stochastic predation system

作　　者：赵玉凤[1] 刘桂荣[2] ZHAO Yufeng;LIU Guirong(School of Computer Science and Information Engineering,Shanxi Technology and Business College,Taiyuan 030006,Shanxi,China;School of Mathematical Sciences,Shanxi University,Taiyuan 030000,Shanxi,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030006 [2]山西大学数学科学学院,山西太原030000

出　　处：《山东大学学报（理学版）》2024年第10期74-88,共15页Journal of Shandong 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”规划课题项目(GH-220495)。

摘　　要：建立一类具有捕食者阶段结构和比率依赖的HollingⅢ型功能反应的随机捕食者-食饵模型。首先,给出了随机模型全局正解的存在唯一性。其次,通过构造合适的Lyapunov函数,利用Has′Minskii的遍历性理论研究了模型的遍历平稳分布的存在唯一性。然后,通过求解相应的三维Fokker-Planck方程的方法,推导出随机捕食模型在正平衡点附近的概率密度函数的精确表达式。最后,通过数值仿真验证了理论结果的合理性。A class of stochastic predator-prey models with predator-stage structure and rate-dependent Holling Ⅲ type functional responses are developed.Firstly,the existence and uniqueness of global positive solutions for stochastic model are obtained.Secondly,the existence and uniqueness of the ergodic stationary distribution are studied by constructing a suitable Lyapunov function and using the ergodic theory of Has′Minskii.Next,by solving the corresponding three-dimensional Fokker-Planck equation,the exact expression of the probability density function of the stochastic predator-prey model near the positive equilibrium point is derived.Finally,the rationality of the theoretical results is verified by numerical simulation.

关 键 词：随机捕食者-食饵模型 平稳分布 阶段结构 比率依赖 概率密度函数 

分 类 号：O175[理学—数学]