一类非自治随机时滞Lotka-Volterra竞争系统的动力学分析  

Dynamical Behavior for a Nonautonomous Lotka-Volterra Competition Model with Stochastic Effects and Time Delays

作　　者：夏源培 杨志春 XIA Yuanpei;YANG Zhichun(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2020年第6期101-107,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11971081);重庆市教育委员会科学技术研究重大项目(No.KJZD-M202000502);重庆市基础与前沿研究项目(No.cstc2018jcyjAX0144);重庆市研究生科研创新项目(No.CYS19290;No.CYS20242)。

摘　　要：[目的]提出一类具有S型分布时滞、随机白噪声以及Markov切换的n维非自治Lotka-Volterra竞争系统,主要研究系统正解的全局存在唯一性、有界性和吸引性。[方法]通过构造适当的Lyapunov函数,利用Ito公式、Chebyshev不等式、指数鞅不等式、Young不等式、大数定理等获得系统解具有全局存在且唯一、随机最终有界的性质。根据Barbalat引理、Holder不等式、矩不等式得到系统正解全局吸引的充分条件。[结果]在任意给定的初值条件下,系统具有全局唯一的解,且该解以概率1停留在R+n中;当时间趋于无穷时系统的解是随机最终有界的且系统几乎所有的样本轨道对于2≥0都是一致连续的;进一步地,当满足■时,系统的任意正解是全局吸引的。[结论]数值实验结果分别验证了系统解的随机最终有界性与全局吸引性。[Purposes] A class of n-dimensional nonautonomous Lotka-Volterra competitive systems with S-type distributed delay,random white noise and Markov switching is proposed.The global existence,uniqueness,boundedness and attractiveness of positive solutions are studied.[Methods]By constructing appropriate Lyapunov functions,and using the Ito formula,Chebyshev inequality,exponential martingale inequality,Young inequality and the law of large numbers,the global existence,uniqueness and the stochastically ultimate boundedness of the system solution are obtained.According to the Barlalat’s lemma,Holder inequality and Moment inequality,the sufficient condition for global attractivity of the system solution is given.[Findings]For any given initial condition,the system has a globally unique solution,and its solution remains in R_+~n with probability 1.Then the solution of the system is stochastically ultimately bounded and the sample paths of X(t) are uniformly continuous for t→∞ a.s..Furthermore,the positive solutions of the system are globally attractive provide that■.[conclusions]An numerical example is given to verify the properties of stochastically ultimate boundedness and global attractivity for the system.

关 键 词：S型分布时滞 白噪声 Markov切换 随机最终有界性 全局吸引性 

分 类 号：O175.14[理学—数学] O175.21[理学—基础数学]