一类具有Holling-Ⅱ功能型反应的随机捕食与被捕食模型的动力学行为分析  

Analysis of the dynamic behavior of a stochastic predation-prey model with Holling-Ⅱ functional response

作　　者：刘朋朋 吴万勤 谭学文[1] LIU Peng-peng;WU Wan-qin;TAN Xue-wen(School of Mathematics and Computer Science,Yunnan Minzu University,Kunming 650031,China)

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650500

出　　处：《云南民族大学学报（自然科学版）》2023年第1期74-82,共9页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(12126363,11261104);云南省基础研究计划项目(202201AT070037).

摘　　要：研究了一类具有第二类功能性反应的随机食饵模型,首先根据利普希兹条件证明模型解的存在性和唯一性,进而证明解的全局性,接着通过构造合适李雅普诺夫函数,利用伊藤公式判断零解的稳定性,最后证明模型的最终行为,主要包括模型平稳分布存在条件和种群灭绝条件.This paper studies a class of stochastic bait models with a second class of functional responses.Firstly,the existence and uniqueness of the model solution are proved according to the Lipschitz condition,and then the global solution is proved.Secondly,the stability of the zero solution is judged by the ITO formula through the construction of suitable Lyapunov function.Finally,the final behavior of the model is proved.It mainly includes the existence condition of model stationary distribution and population extinction condition.

关 键 词：利普希兹条件 解的存在性和唯一性 李雅普诺夫函数 伊藤公式 零解的稳定性 平稳分布 灭绝 

分 类 号：O211.63[理学—概率论与数理统计]