摘要
考虑传染病对捕食-被捕食者都具有致病作用的一类时滞捕食-被捕食模型,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u=1τ+τ2适当小时,边界平衡点E3是局部渐近稳定的,随着时滞的增加,E3由稳定变为不稳定,系统在E3附近发生Hopf分支;当时滞1τ+2τ2充分小时,边界平衡点E2=(1,0,0)是全局稳定的.
A system of retarded functional differential equations is proposed as a predator- prey model with disease in the prey and predator. The invariance of none - negativity, nature of boundary equilibria and global stability are analyzed. The author shows that boundary equilibrium E3 is locally asymptotically stable when time delays u u=τ1+τ2 is suitable small, while a loss of stability by a Hopf bifurcation can occur as the delays increase, and shows that boundary equilibrium E2 = ( 1,0,0) is global stability when time delay τ1+τ2 is suitable small.
出处
《安徽大学学报(自然科学版)》
CAS
北大核心
2007年第4期5-8,共4页
Journal of Anhui University(Natural Science Edition)
基金
南昌大学科研基金资助项目(2006Z03371)