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

作　　者：魏新[1] 李冬松[2] 张敬[1] 

机构地区：[1]齐齐哈尔大学理学院,齐齐哈尔161006 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2013年第1期79-82,共4页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省教育厅科学技术研究项目(12511609);齐齐哈尔大学青年教师科研启动支持计划项目(2012k-M31)

摘　　要：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.

关 键 词：双时滞 欧拉方法 数值逼近 HOPF分支 

分 类 号：O175[理学—数学]