具双时滞的Nicholson果蝇系统的动力学性质

张向华^1,2

1.哈尔滨工业大学理学院;2.黑龙江科技学院理学院



摘要:

为更好地维护生态系统和谐与稳定,研究了具双时滞的Nicholson果蝇动力系统的稳定性.对系统在正平衡点附近的稳定性,局部Hopf分支的存在性,发生条件、Hopf分支的方向,分支周期解的稳定性以及分支随参数变化其周期解的周期变化进行了讨论.然后通过数值模拟有力地支撑了前面分析得到的理论结果,并且得到在正平衡点附近Hopf分支的全局存在性.用分支理论解释了生态系统得以循环不息的原因.

关键词:  平衡点  稳定性  周期解  Hopf分支

DOI：10.11918/j.issn.0367-6234.2011.06.015

分类号:O175.13

基金项目:黑龙江省自然科学基金资助项目(A201015)



Dynamical analysis in Nicholson blowflies system with two delays

ZHANG Xiang-hua^1,2

1.School of Science,Harbin Institute of Technology,150001 Harbin,China;2.Science of College,Heilongjiang Institute Science and Technology,150027 Harbin,China

Abstract:

In order to maintain the harmony and stability of ecosystems,in this paper,the stability of Nicholson’s blowflies model with time delay was investigated.The distribution of the characteristic roots,the stability of the equilibrium,the existence of Hopf bifurcation and its conditions were discussed.Meanwhile,some simulations were carried out,which supported the theoretical results obtained previously and the global existence of Hopf bifurcation near the positive equilibrium point was got.At last,the reasons of circulating ecosystems were explained by the bifurcation theory.

Key words:  equilibrium point  stability  periodic solutions  Hopf bifurcation