一类具有外部食物资源和随机干扰的非自治捕食与被捕食模型动力学研究（英文）  

Dynamics of a Stochastic Non-Autonomous Prey-Predator Model with Outside Food Resource

作　　者：惠洪文 聂麟飞[1] HUI Hongwen;NIE Linfei(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《应用数学》2019年第1期1-10,共10页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11461067,11771373);the Natural Science Foundation of Xinjiang(2016D01C046,2016D03022);the Scientific Research Programmes of Colleges in Xinjiang(XJEDU2017T001)

摘　　要：本文提出一类具有外部食物资源和季节转换的随机Lotka-Volterra捕食模型,得到模型全局正解的存在性与有界性.进一步,通过采用构造合适的Lyapunov函数、比较原理等方法,分别得到模型周期解的存在性与全局吸引性、种群的持久性与灭绝性,并讨论了白噪声对种群的影响.In this paper, we propose a stochastic Lotka-Volterra model with seasonal variation and outside food resource, and the existence of global positive solution and boundedness are derived. Further, by constructing some suitable Lyapunov functions, we show that there is at least one periodic solution and analyze the relation between the species densities and white noise. In addition, we get some sufficient conditions for the extinction,strong persistence in the mean and persistence of populations in the sense, respectively.Finally, the global attractiveness of solution of this model is discussed.

关 键 词：随机的Lotka-Volterra模型 季节转换 周期解 持久性与灭绝性 全局吸引性 

分 类 号：O175.14[理学—数学]