一类具连续时滞的三种群互助模型正平衡态的渐近稳定性  

Global Asymptotic Stability of Positive Equilibrium in a 3-Species Cooperating Models with Continuous Time Delays

作　　者：王长有[1,2] 杨春德[1] 王术[2] 刘玉记[3] 

机构地区：[1]重庆邮电大学应用数学研究所,重庆400065 [2]北京工业大学应用数理学院,北京100124 [3]广东商学院数学与计算科学系,广州510320

出　　处：《生物数学学报》2008年第4期639-646,共8页Journal of Biomathematics

基　　金：重庆市教育委员会科学技术研究项目(KJ080511);重庆市科委自然科学基金计划项目(CSTC;2008BB7415);广东省自然科学基金项目(NO.7004569)

摘　　要：本文研究了一类具连续时滞的三种群互助模型,利用上、下解方法及相应的单调迭代方法,获得了该系统存在唯一正常数平衡态及该平衡态是全局渐近稳定的结论,为讨论时滞三种群模型提供了一种有效方法,所得结果也适用于二种群互助模型及不含时滞和扩散项的互助模型,因而推广了已有的一些结论.This paper is concerned with a 3-species cooperating model with continuous delays. The goal of the paper is to prove the global asymptotic stability of a positive steady-state solution for the model problem. The result of global asymptotic stability implies that the model system coexists, is permanent. Our approach to the problem is based on the method of upper and lower solutions for a more general reaction-diffusion system that gives a common framework for the 3-species model problems. Some global stability results for the 2-species cooperating reaction -diffusion systems and 3-species cooperating models without delays are included in the discussion.

关 键 词：三种群互助模型 渐近稳定性 连续时滞 正平衡态 上 下解 

分 类 号：O175.29[理学—数学]