具有时滞的生态-流行病模型的稳定性和Hopf分支  

Stability and Hopf Bifurcation of an Eco-epidemiological Model with Delays

作　　者：宋新宇[1] 肖燕妮[2] 陈兰荪[2] 

机构地区：[1]信阳师范学院数学系,河南信阳464000 [2]中国科学院数学与系统科学研究院,北京100080

出　　处：《数学物理学报（A辑）》2005年第1期57-66,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(10471117);河南省高校杰出科研人才创新工程项目

摘　　要：该文考虑一类食饵染病的时滞捕食-被捕食模型.作者分析了系统的非负不变性,边界平衡点的性质和全局稳定性.证明了当时滞τ=τ1+τ2适当小时,正平衡点是局部渐近稳定的,随着时滞的增加,正平衡点由稳定变为不稳定,系统在正平衡点附近发生Hopf分支.A system of retarded functional differential equations is proposed as a predator-prey model with disease in the prey. The invariance of non-negativity, nature of boundary equilibria and global stability are analyzed. The authors show that positive equilibrium is locally asymptotically stable when time delays τ=τ-1+τ-2 is suitable small, while a loss of stability by a Hopf bifurcation can occur as the delays increase.

关 键 词：捕食模型 全局稳定性 HOPF分支 

分 类 号：O175.1[理学—数学]