摘要
研究了一类具有时滞的HIV体内感染模型,引入了以受感染T*细胞释放出病毒的持续时间为时滞参数.通过Routh-Hurwitz准则和构造Lyapunov函数及对系统非负不变性分析,得出边界平衡点具有全局稳定性.并证明了存在临界值τ0,当τ<τ0时,内部平衡点是局部渐近稳定的;当τ>τ0时,内部平衡点是不稳定的;当τ=τ0时,系统具有Hopf分支.最后利用Matlab软件进行数值模拟并验证了分析的合理性.
The HIV infection in vivo model with time delay is studied,which incorporates the duration for the infected T＊ cells to release the virus as the delay parameter.The global stability of the boundary equilibria is obtained by using the Routh-Hurwitz criteria,constructing Lyapunov function and the nonnegative invariance analysis of the system.And the existence of the threshold τ0 is proved,the inner equilibria is local asymptotic stable as ττ0;the inner equilibria is unstable as τ=τ0,it appears a Hopf bifurcation in the system as τ τ0.At last the numerical simulation is given with the Matlab software,and the rationality of the theoretical analysis is verified.
出处
《西安工程大学学报》
CAS
2011年第1期104-112,共9页
Journal of Xi’an Polytechnic University
关键词
时滞
HIV
稳定性分析
HOPF分支
数值模拟
time delay
HIV
stability analysis
Hopf bifurcation
numerical simulation
