一类非自治随机互惠系统的渐近性态  

Asymptotic Behavior of a Non-Autonomous Stochastic Mutualism System

作　　者：郭奥 丁孝全 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳

出　　处：《理论数学》2019年第4期514-526,共13页Pure Mathematics

基　　金：国家自然科学基金项目(11271110);河南省教育厅科技攻关项目(15A120009)的支持。

摘　　要：本文讨论一类非自治随机互惠系统的渐近性态。首先,对任意正初值,建立了系统全局正解的存在唯一性。接着,利用随机微分方程比较定理和Lyapunov函数,得到了系统的持续性、灭绝性、全局吸引性和周期解的存在性。最后,数值模拟验证了理论结果的合理性。This paper is devoted to the asymptotic behavior of a non-autonomous stochastic mutualism system.Firstly,the existence and uniqueness of global positive solution to the system is established for any positive initial value.Then by using the comparison theorem for stochastic differential equations and Lyapunov functions,the sufficient conditions for the permanence,extinction,global attractivity,and existence of periodic solutions to the system are derived respectively.Finally,some numerical simulations are given to illustrate our theoretical results.

关 键 词：随机互惠系统 全局吸引性 持续性 灭绝性 周期解 

分 类 号：O1[理学—数学]