变时滞随机Lotka-Volterra生物模型的渐近性质  

Asymptotic properties of the stochastic Lotka-Volterra system with variable time delay

作　　者：胡军浩[1] 王朝航 HU Junhao;WANG Zhaohang(College of Mathematics and Statistics,South-Central Minzu University,Wuhan 430074,China)

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2023年第3期402-407,共6页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(61876192);中南民族大学研究生学术创新基金项目(3212023sycxjj003)。

摘　　要：研究了变时滞随机Lotka-Volterra(LV)生物模型,其中变时滞函数是不可微的,放宽了现有文献变时滞是可微且导数小于1的假设.使用Itô公式和线性矩阵不等式(LMI)研究了这类生物模型全局正解的存在性和唯一性,并进一步给出了其正解渐近有界、时间均值意义下矩有界和多项式增长的充分条件.最后给出实例验证了结论的有效性.This paper is concerned with stochastic Lotka-Volterra(LV)system with variable time delay.Comparing with most existing papers,the time delay functions in the LV system are no longer required to be differentiable,their derivatives are less than 1 is not to be mentioned.The existence and uniqueness of the global positive solutions of this system are investigated by usingItôformula and linear matrix inequality(LMI).Further,sufficient conditions are also obtained for the asymptotic boundedness,time average moment boundedness and the polynomial pathwise growth of the positive solution.Finally,an example is given to illustrate the effectiveness of the results.

关 键 词：随机生物模型 Lotka-Volterra生物模型 不可微时滞函数 LMI不等式 渐近有界性 

分 类 号：O241.8[理学—计算数学]