具有脉冲扰动的随机New Logistic模型的动力学行为  

Dynamic behavior of stochastic New Logistic model with impulsive perturbation

作　　者：李鹏喆 艾晓辉[1] LI Pengzhe;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》2022年第6期640-648,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11401085);中央高校基础科研资助项目(2572021DJ04);黑龙江省博士后资助项目(LBH-Q21059)。

摘　　要：对于食物中受环境干扰的微生物生长的动力学问题,根据随机微分方程理论,在New Logistic模型的基础上,引入白噪声和脉冲干扰,提出了具有脉冲扰动的随机New Logistic模型,并研究了模型的动力学行为。首先证明了模型全局正解的存在性,其次分析了模型解的弱持久性,再次利用伊藤公式和切比雪夫不等式证明了模型解的随机持久性,最后通过数值模拟验证了理论结论。Aiming at the problem of dynamics of microbial growth disturbed by environment in food,according to the theory of stochastic differential equations,based on the New Logistic model,the stochastic New Logistic model with impulsive perturbation is proposed by introducing white noise and impulsive disturbance,and the dynamic behavior of the model is studied.Firstly,the existence of the global positive solution of the model is proved.Secondly,the weak persistence of the model is analyzed.Thirdly,the stochastic persistence of the model is proved by using Itôformula and Chebyshev inequality.Finally,the theoretical conclusions are verified by numerical simulation.

关 键 词：随机模型 脉冲扰动 全局正解 弱持久性 随机持久性 

分 类 号：O211.63[理学—概率论与数理统计]