一类具有脉冲的Nicholson果蝇模型周期解的存在性和全局吸引性

EXISTENCE AND GLOBAL ATTRACTIVITY OF POSITIVE PERIODIC SOLUTIONS FOR THE NICHOLSON'S BLOWFLIES MODEL WITH IMPULSES

研究了下列具有脉冲现象的Nicholson果蝇模型{N′(t)=-δ(t)N(t)+p(t)N(t-mω)e-a(t)N(t-mω),t>0,t≠tkN(tk+)-N(tk)=bkN(tk),k=1,2,…的正周期解～N(t)的存在性问题及其部分动力学行为.当m=0时,得到上述方程存唯一正周期解N～(t),并且是全局渐近稳定的;当m≠0时,给出了～N(t)是全局吸引的充分条件.

In this pater,we consider the following nonlinear impulsive delay Nicholson＇s blowflies model{N＇（t）=-δ（t）N（t）＋p（t）N（t-mω）e-a（t）N（t-mω）,t〉0,t≠tkN（t＋k）-N（tk）=bkN（tk）,k=1,2,…,we can get the existence and some dynamical behaviors of the positive periodic solution（t）.In the nondelay case（m=0）,we show that model has a unique positive periodic solution N～（t） which is globally asymptotically stable.In the delay case（m≠0）,we present sufficient conditions for the global attractivity of N～（t）.