具双时滞Nicholson果蝇系统的数值逼近

Numerical approximation of a class Nicholson’s blowflies model with two delays

研究一类带有捕捞项的具有双时滞的Nicholson果蝇系统的数值逼近问题。采用欧拉方法,得到相应的离散果蝇系统,将该时滞差分方程表示为映射,然后利用离散动力系统的分支理论,给出该离散果蝇系统的数值Hopf分支存在的充分条件。证明当步长充分小时,离散果蝇系统的数值Hopf分支值逼近于相应连续果蝇系统的Hopf分支值。

The numerical approximation of a class Nicholson＇s blowflies model with harvesting rate and two delays is studied. First, discrete system is gained by using Euler method and the delay deference equation is written as a map. Then, employing the theories of bifurcation for discrete blowflies system, the sufficient conditions to guarantee the existence of Hopf bifurcations for numerical approximation are given. It also proved that for sufficient small step, the numerical Hopf bifurcation value is approximate to that of the original equation.