一类具有Ornstein-Uhlenbeck过程的水母模型  

A Class of Jellyfish Model with Ornstein-Uhlenbeck Process

作　　者：梁春叶 王清龙 郭俞红 刘志军 LIANG Chunye;WANG Qinglong;GUO Yuhong;LIU Zhijun(School of Mathematics and Statistics,Hubei Minzu University,Enshi 445000,China)

机构地区：[1]湖北民族大学数学与统计学院,湖北恩施445000

出　　处：《湖北民族大学学报（自然科学版）》2024年第2期267-275,共9页Journal of Hubei Minzu University:Natural Science Edition

基　　金：国家自然科学基金项目(12101211);湖北省自然科学基金项目(2023AFB1095);湖北民族大学研究生科研创新项目(MYK2024076);湖北民族大学数学与统计学院研究生教育创新项目(STK2023007)。

摘　　要：为探究随机扰动对水母种群动力学行为的影响,考虑环境噪声扰动建立了一类具有Ornstein-Uhlenbeck过程的水母模型。首先分析了模型全局解的存在唯一性,并采用Lyapunov函数方法给出了水母灭绝性的充分条件。其次利用Khasminskii理论得到了模型平稳分布存在性的充分条件。最后通过具体的数值例子验证了理论结果的可行性。结果表明,回复速率的增大或环境波动强度的减小都会加快水母种群的灭绝速率,这意味着可以通过适当调节回复速率的大小或环境波动的强度来控制水母种群的增长。该研究可为制定水母暴发防治策略提供一定的理论参考。With the idea of environmental noises,a jellyfish model perturbed by the Ornstein-Uhlenbeck process was developed to investigate the effects of random perturbations on the dynamic behavior of jellyfish populations.Firstly,global solution of the model was analyzed and sufficient condition for the extinction of jellyfish was given by the Lyapunov function method.Secondly,by using the Khasminskii theory,sufficient condition for the existence of the stationary distribution of the model was obtained.Finally,several specific numerical examples were employed to validate the theoretical findings.The results indicate that the increasing of the speed of reversion or the decreasing of the intensity of volatility can both accelerate the extinction rate of jellyfish populations,which means that the growth of jellyfish populations can be controlled by appropriately adjusting the magnitude of the speed of reversion or the intensity of volatility.The proposed model provides some theoretical results for designing control strategies for jellyfish outbreaks.

关 键 词：随机水母模型 ORNSTEIN-UHLENBECK过程 LYAPUNOV函数方法 Khasminskii理论 灭绝性 平稳分布 

分 类 号：O175[理学—数学]