食饵具有Smith增长且基于比率依赖捕食系统模型的定性分析  

Qualitative Analysis of A Ratio-Dependent Predator-Prey System with Smith Growth for Prey

作　　者：韩二东[1] 郭鹏[1] 

机构地区：[1]西北工业大学管理学院,陕西西安710072

出　　处：《生物数学学报》2015年第3期549-557,共9页Journal of Biomathematics

基　　金：国家自然科学基金项目(71272049)

摘　　要：研究一类食饵为Smith增长且基于比率依赖的HollingⅢ型功能反应捕食系统模型,运用示性方程讨论参数变化时奇点(0,0)邻域内轨线的走向,给出系统平衡点为全局吸引子或吸引子的充分条件,得到系统正周期解的不存在性、正平衡点的全局渐近稳定性及系统存在极限环的充分条件.The ratio-dependent predator-prey system with Holling type-Ill functional response was proposed,where the Smith growth for prey.When the parameters changed,asymptotic behaviors of the singular point(0,0) was discussed by using the characteristic equation.Then sufficient conditions were derived from whether the system equiUbriums are global attractors or attractors.Sufficient conditions were derived from the inexistence of positive periodic,the global asymptotic stability of the positive equilibrium point and existence of the limit cycle.

关 键 词：比率依赖 高阶奇点 吸引子 全局渐近稳定 极限环 

分 类 号：O175[理学—数学]