具双时滞的Nicholson果蝇系统的动力学性质

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.%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.