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
赵玉凤 1刘桂荣2
作者信息
- 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
- 折叠
摘要
建立一类具有捕食者阶段结构和比率依赖的Holling Ⅲ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.
Abstract
A class of stochastic predator-prey models with predator-stage structure and rate-dependent Holling Ⅲ type functional re-sponses 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 expres-sion 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Key words
stochastic predator-prey model/stationary distribution/stage structure/ratio-dependent/probability density function引用本文复制引用
基金项目
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)
出版年
2024
NETL
NSTL
万方数据