研究状态机制转换下带有食饵避难响应的随机Leslie-Gower捕食模型  

Stochastic Leslie-Gower Predator-Prey Model with a Prey Refuge under Regime Switching

作　　者：焦媛 靳海娟[1] 张秀锋 JIAO Yuan;JIN Hai-juan;ZHANG Xiu-feng(Department of Mathematics,Changzhi College,Changzhi Shanxi,046011)

机构地区：[1]长治学院数学系,山西长治046011

出　　处：《山西大同大学学报（自然科学版）》2021年第3期38-44,共7页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：长治学院校级科研课题[XJ202000161]。

摘　　要：针对生物种群中存在的带有食饵避难响应的Leslie-Gower捕食模型加入噪声项以及状态突变的马尔可夫链,运用伊藤公式、比较定理、马尔科夫链的遍历理论以及鞅的强大数定律等,研究其正解的存在唯一性、有界性以及持久性和灭绝性,表明此操作的可持续性和稳定性。For Leslie-Gower predator model with prey refuge response and adding noise term Markov chain state of mutation,we used Ito formula,comparison theorem,ergodic theory of Markov chains and the strong law of martingale,etc.to study the exis-tence uniqueness,boundedness and persistence and extinction of its positive solutions,and showed the sustainability and stability of this operation.

关 键 词：Leslie-Gower模型 伊藤公式 马尔科夫链的遍历理论 鞅的强大数定律 

分 类 号：O193[理学—数学]