带Beddington-DeAngelis功能反应项的捕食者-食饵扩散模型的稳定性  

Stability of a Diffusive Predator-Prey Model with Beddington-DeAngelis Functional Response

作　　者：许生虎[1] 伏升茂[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《应用数学》2008年第2期345-353,共9页Mathematica Applicata

基　　金：国家自然科学基金(10471157);甘肃省自然科学基金(3ZS061-A25-015);甘肃省教育厅科研项目(0601-21);西北师范大学创新工程项目资助(NWNU-KJCXGC-03-39)

摘　　要：本文首先应用上下解方法讨论一类带Beddington-DeAngelis功能反应项的捕食者-食饵扩散模型解的一致有界性和整体存在性,然后通过线性化方法分别给出该模型的半平凡平衡点和正平衡点局部渐近稳定的充分条件,最后应用Lyapunov泛函方法讨论唯一正平衡点的全局渐近稳定性.In this paper, using the upper and lower solutions method,the uniform boundedess and global existence of solutions to the predator-prey diffusion system with Beddington-DeAngelis functional response are investigated. Meanwhile, sufficient conditions of the local asymptotical stability of the semitrivial equilibrium and the positive equilibrium point are given by linearization, respectively. The global asymptotical stability of the unique positive equilibrium point is also given by Lyapunov function.

关 键 词：捕食者-食饵模型 局部/全局渐近稳定性 Beddington-DeAngelis功能反应函数 

分 类 号：O175.26[理学—数学]