摘要
讨论了一类具有时滞的干扰的单种群模型的无条件稳定性以及Hopf分支的存在唯一性。首先,利用特征值理论得到了模型无条件稳定性的充要条件,从而说明时滞为无害时滞;再以时滞τ为参数,给出了Hopf分支的存在唯一性及分支值处模型平衡态的稳定性的条件;最后举例验证了定理的可实现性,利用Matlab得到其参数取不同值时的曲线拟合图。
The unconditional stability and existence of a unique Hopf bifurcation are discussed for a class of interence model with delay.First of all,the sufficient and necessary condition of unconditional stability is obtained according to the eigenvalue theory.Consequently it is implied that the time delay is harmless one.Then the condition of existence of a unique Hopf bifurcation and stability of equilibrium state in bifurcation values is derived when time delay is a parameter.In the end,the achievability of the theorems is verified by examples.The fitted curves are achieved by Matlab when assign the different parmaters to the model.
出处
《湖北师范学院学报（自然科学版）》
2011年第3期65-70,共6页
Journal of Hubei Normal University(Natural Science)
关键词
时滞干扰模型
HOPF分支
无条件稳定性
interference model with time delay
Hopf bifurcation
unconditional stability
