一类带白噪声和Lévy跳跃的营养-浮游植物模型的分析  

Analysis of a Nutrient-Phytoplankton Model with White Noise and Lévy Jumps

作　　者：谭杨[1] 郭子君[2] 杨林 王海扬[1] TAN Yang;GUO Zijun;YANG Lin;WANG Haiyang(Tongren Polytechnic College, Tongren 554300, China;Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510275, China)

机构地区：[1]铜仁职业技术学院,贵州铜仁554300 [2]华南农业大学理学院应用数学研究所,广东广州510275

出　　处：《中北大学学报（自然科学版）》2022年第3期193-199,208,共8页Journal of North University of China(Natural Science Edition)

基　　金：铜仁市科技计划项目(铜市科研[2020]116号);广东省自然科学基金资助项目(2015A030310065)。

摘　　要：研究了一类带有随机白噪声干扰及Lévy跳的营养-浮游植物模型.首先利用停时等方法证明了模型全局解的存在及其唯一性;然后得到了浮游植物种群趋于灭绝及依平均持久的充分条件,结果显示,只要随机干扰的强度足够大,则浮游植物种群几乎处处趋于灭绝;最后对灭绝性和持久性的结果进行了数值模拟.A nutrient-phytoplankton model with random white noise and Lévy jump was studied.Firstly,the existence and uniqueness of the global solution of the model are proved by using the stopping time method.Then,the sufficient conditions for the phytoplankton population to become extinct and persistent in the mean are obtained and the results showed that as long as the intensity of random disturbance is large enough,the phytoplankton population tends to extinct almost sure.Finally,the numerical simulation about the obtained results of extinction and persistence was carried out.

关 键 词：营养-浮游植物模型 随机Lyapunov函数 灭绝性 依平均持续存在 

分 类 号：O211.61.2[理学—概率论与数理统计]