具有病毒感染的Holling-Tanner捕食-食饵模型的定性分析  

Qualitative Analysis for a General Holling-Tanner Predator-prey Model with Disease Infection

作　　者：王治国[1] 李博[1] 吴建华[1] 

机构地区：[1]f陕西师范大学数学与信息科学学院,西安710062

出　　处：《工程数学学报》2011年第1期75-80,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10571115);教育部高等学校博士点基金(200807180004);陕西省自然科学基础研究资助项目(2007A11)~~

摘　　要：利用稳定性理论,讨论了一类带扩散项食饵染病的捕食-食饵模型正常数解的一致渐近稳定性,得出一定条件下,在常数解的某个邻域内系统不存在非常数正解的结论.同时,利用极值原理和分歧理论,研究了正平衡解的上下界估计和非常数正解的存在性.文中的结果表明,在一定的条件下,受病毒影响的捕食,食饵种群是可以共存的.By using the stability theory,the uniform asymptotical stability of the positive constant solution is discussed for a general predator-prey model with diffusion items and disease in the prey.It is shown that there is no non-constant positive solution in some neighborhood of the positive constant solution under certain conditions.In addition,the prior estimate and the existence of the positive steady states are given by using the maximum principle and the bifurcation theory.The result shows the persistence of species can be ensured under certain conditions.

关 键 词：渐近稳定 平衡态 分歧 

分 类 号：O175.26[理学—数学]