亚纯函数奇异方向的讨论

一、引 言 作者已经证明 定理A设f(z)为开平面上p(0<p<+∞)级亚纯函数,p(r)是共一精确级,U(r)=r^(p(r)),则存在一条从原点发出的牛直线B:argz=θ_0(O≤θ_0<2π),对一切开平面上的亚纯函数a(z),T(r,a(z))=o{U(r)}(我们规定a(z)≡∞为特征恒为零的亚纯函数)与正数ε。

Globally asymptotic stability of a predator-prey model with stage structure incorporating prey refuge

This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.