具有Lévy跳的随机Lotka-Volterra互惠系统的渐近行为  

The asymptotic behavior of a stochastic Lotka-Volterra mutualism system with Lévy jumps

作　　者：秦剑利 刘桂荣[1] QIN Jianli;LIU Guirong(School of Mathematical Sciences,Shanxi University,Taiyuan,Shanxi 030006,China)

机构地区：[1]山西大学数学科学学院

出　　处：《贵州师范大学学报（自然科学版）》2019年第6期78-82,113,共6页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金(11471197);山西省自然科学基金(201601D202002)

摘　　要：针对一类具有Lévy跳的随机Lotka-Volterra互惠系统的渐近行为,首先通过构造Lyapunov函数证明了系统全局正解的存在唯一性。然后应用广义的It公式与指数鞅不等式等方法,得到系统的随机最终有界性与灭绝性。最后通过数值模拟验证了理论结果的合理性。For a class of the asymptotic behavior of stochastic Lotka-Volterra mutualism system with Lévy jumps,we proved the existence and uniqueness of the global positive solution by constructing Lyapunov function.Then the stochastically ultimate boundedness and extinction of this system are obtained by means of generalized It formula and exponential martingale inequality.Finally,numerical simulations are carried out to verify the rationality of the theoretical results.

关 键 词：LOTKA-VOLTERRA系统 Lévy跳 灭绝 随机最终有界 

分 类 号：O211.63[理学—概率论与数理统计]