中山大学学报自然科学版 ›› 2010, Vol. 49 ›› Issue (2): 48-52.

• 研究论文 • 上一篇    下一篇

基于比率依赖的两种群捕食者—食饵系统的随机模型

郭子君
  

  1. (华南农业大学应用数学研究所,广东 广州 510642)
  • 收稿日期:2009-01-07 修回日期:1900-01-01 出版日期:2010-03-25 发布日期:2010-03-25

A Stochastic Models on PredatorPrey Systemof Two Species with RatioDependence

GUO Zijun   

  1. (Institute of Applied Mathematics, SouthChina Agriculity University, Guangzhou 510642, China)
  • Received:2009-01-07 Revised:1900-01-01 Online:2010-03-25 Published:2010-03-25

摘要: 研究一类比率依赖的两种群捕食者-食饵系统的随机模型。利用随机微分方程理论,通过构造Lyapunov泛函,并结合停时分析、不等式构造等技巧,证明了比率依赖的两种群捕食者—食饵随机系统整体解的存在唯一性,整体解的有界性与渐近性质。

关键词: 捕食者-食饵系统, Brownian运动, 随机微分方程, 整体解, K.itó公式

Abstract: A class of predatorprey system of two species with ratiodependence is studied. According to the theory on stochastic differential equation, by constructing the Lyapunov function, and combining with stopping time and some analysis techniques, the existence and uniqueness of global solution for the system are proved. The boundedness and asymptotic estimate of the global solution are also discussed.

Key words: predatorprey system, Brownian motion, stochastic differential equation, global solution, K.itó formula

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