均值回归OU过程驱动的具有有限Markov链和Lévy跳的随机Gilpin-Ayala模型的动力学研究
Dynamics of stochastic Gilpin-Ayala model with finite Markov chain and Lévy jumps driven by mean-reverting OU process
高蒙 1艾晓辉1
作者信息
- 1. 东北林业大学理学院,哈尔滨 150040
- 折叠
摘要
提出了均值回归OU(Ornstein-Uhlenbeck)过程驱动的具有有限Markov链和Lévy跳的随机Gilpin-Ayala模型,并研究了该随机Gilpin-Ayala模型的渐近行为.首先,选用适当的李雅普诺夫函数,证明随机Gilpin-Ayala种群模型全局解的存在性;其次,证明了随机Gilpin-Ayala种群模型解的矩有界性;再次,证明了随机Gilpin-Ayala种群模型解的平稳分布的存在性;最后,证明了随机Gilpin-Ayala种群模型的灭绝性.通过例子和数值模拟图验证了理论结果.
Abstract
A stochastic Gilpin-Ayala model with finite Markov chain and Lévy jumps driven by mean-reverting OU(Ornstein-Uhlenbeck)process was proposed and asymptotic behaviors of the stochastic Gilpin-Ayala model were studied.Firstly,the existence of the global solution of the stochastic Gilpin-Ayala population model was proved by selecting an appropriate Lyapunov function.Secondly,the moment boundedness of the solution to the stochastic Gilpin-Ayala population model was given.Then the existence of a stationary distribution of solutions for the stochastic Gilpin-Ayala population model was proved.Finally,the extinction of the stochastic Gilpin-Ayala population model was proved.The theoretical results were verified through numerical examples and numerical simulations.
关键词
随机Gilpin-Ayala模型/OU过程/平稳分布/灭绝性Key words
stochastic Gilpin-Ayala model/OU process/stationary distribution/extinction引用本文复制引用
基金项目
国家自然科学基金资助项目(11401085)
黑龙江省博士后科学基金资助项目(LBH-Q21059)
中央高校基本科研业务费专项资金项目(2572021DJ04)
出版年
2024
NETL
NSTL
万方数据