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中文摘要：
研究了一类具有时滞和干扰的单种群模型的稳定性与Hopf分支问题.由特征值理论得到模型的正平衡态局部无条件渐进稳定的充要条件;以时滞τ为参数,得出模型存在Hopf分支的条件及分支值,并讨论了分支值处模型的正平衡态的稳定性;最后根据实例利用Matlab画出模型的数值解的图像,结合图像讨论了各参数变化对分支周期解的影响.
英文摘要：
The Hopf bifurcation and stability for a class of single-speices model with interference and delays are investigated.Sufficient conditions of locally asymtotic stability of the modle are derived by using the characteristic value theory.Considering the delay τ as a parameter,conditons of the existence of Hopf bifurcation and the bifurcation value and its stability are obtained.Finally fitting maps about the examples are presented by using Matlab and the effects of the parameters on bifurcation periodic solutions are disscused.
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