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

作　　者：高蒙 艾晓辉[1] GAO Meng;AI Xiaohui(School of Science,Northeast Forestry University,Harbin 150040,China)

机构地区：[1]东北林业大学理学院,哈尔滨150040

出　　处：《黑龙江大学自然科学学报》2024年第4期392-405,共14页Journal of Natural Science of Heilongjiang University

基　　金：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)。

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。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 

分 类 号：O211.63[理学—概率论与数理统计]