环境噪声影响下的时滞对数人口模型  

Delay Logarithmic Population Model under the Influence of Environmental Noise

作　　者：张若军[1] 戴楠 ZHANG Ruojun;DAI Nan(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,青岛266100

出　　处：《应用泛函分析学报》2020年第3期133-140,共8页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(10771014);中央高校基本科研业务费专项基金(201964008)。

摘　　要：本文考虑了一类在环境噪声影响下的时滞对数人口模型.首先,在噪声强度的某些条件下,应用Itô公式和不等式技巧证明了描述这个模型的随机泛函微分方程全局正解的存在唯一性.其次,推导了该方程最终有界性的几个结果,并估计了解的Lyapunov指数.最后,给出了一个例子及数值仿真,说明了本文得到结论的有效性.In this paper,a class of delay logarithmic population model under the influence of environmental noise is considered.Firstly,under some conditions of noise intensity,the existence and uniqueness of the global positive solution for the stochastic functional differential equation describing the model are proved by using Itôformula and inequality technique.Secondly,several kinds final boundedness of the equation are derived and the Lyapunov exponent of the solution is estimated.Finally,an example and numerical simulation are given to illustrate the effectiveness of our conclusions.

关 键 词：时滞对数人口模型 环境噪声 布朗运动 最终有界性 Itô 公式 

分 类 号：O211.63[理学—概率论与数理统计]