食饵具庇护所的基于比率捕食-食饵模型的全局稳定性和分支  

Global Stability and Bifurcation of a Ratio-Dependent Predator-Prey Model with Prey Refuge

作　　者：陈柳娟[1] 陈凤德[2] 

机构地区：[1]福建教育学院理科研修部,福州350025 [2]福州大学数学与计算机科学学院,福州350108

出　　处：《数学学报（中文版）》2014年第2期301-310,共10页Acta Mathematica Sinica：Chinese Series

基　　金：福建省自然科学基金(2011J01007);福建省科技创新平台计划资助项目(2009J1007)

摘　　要：研究一类食饵具庇护所的基于比率捕食-食饵模型,得到该模型的全局稳定、极限环以及Hopf分支等的一系列充分条件.研究表明当模型捕食种群转化率、死亡率和半饱和常数满足一定条件时,食饵庇护量不影响捕食、食饵两种群的共存.一旦该条件不满足,则食饵庇护量具有稳定化作用.数值模拟验证了所得结论的可行性.A ratio-dependent predator-prey model incorporating a prey refuge is in vestigated and a series of sufficient conditions on global stability, limit cycle and Hopf bifurcation are obtained. The results show that when the transformation rate, mortal- ity and the half-saturation constant of predator population satisfy certain conditions,prey refuge has no influence on the coexistence of predator and prey species. Once the condition is not satisfied, then prey refuge has stabilization effect. Numerical simula tions are performed to illustrate the feasibility of our results.

关 键 词：食饵庇护所 HOPF分支 transcritical分支 全局稳定 极限环 

分 类 号：O175.12[理学—数学]