一类含时滞的广义Logistic模型的Hopf分支

The Hopf bifurcation of a class of general Logistic model with time delay

讨论了具有时滞的广义Logistic模型分支周期解的存在性、稳定性及近似分支周期解.用周期函数正交性方法得到了该模型具有Hopf分支的条件及其近似分支周期解的表达式,绘图验证了定理的可实现性,讨论了参数对周期解的周期和振幅的影响.

The existence, stability and the approximate bifurcation periodic solution of a class of general Logistic model with time delay are discussed. Using the orthogonal method of period function, the conditions that the model contains bifurcation periodic solution and the form of the approximate bifurcation periodic solution are obtained. The achievability of the theorem is proved across drawing the graph of the periodic solution. Finally, the effect of parameters on the amplitude of vibration and the period of the periodic solution are discussed.