Global stability of a delayed ratio-dependent predator-prey model with Gompertz growth for prey

A delayed ratio-dependent predator-prey model with Gompertz growth for prey is investigated. The local stability of a predator-extinction equilibrium and a coexistence equilibrium is discussed. Furthermore, the existence of Hopf bifurcation at the coexistence equilibrium is established. By constructing a Lyapunov functional, sufficient conditions are obtained for the global stability of the coexistence equilibrium.     

一类具有阶段结构的Holling Ⅱ型捕食系统的一致持久性

讨论了一类捕食者分为幼虫、成虫两个阶段,具有比率依赖的Ho llingⅡ型功能反应函数的捕食系统的一致持久性,利用比较原理给出了系统是一致持久的充分条件.     

Blow-up,quenching, aggregation and collapse in a chemotaxis model with reproduction term

In this paper,we consider the following chemotaxis model with ratio-dependent logistic reaction term u/t=D▽(▽u-u▽ω/ω)+u(α-bu/ω),(x,t)∈QT,ω/t=βu-δω,(x,t)∈QT,u▽㏑(u/w)·=0,x ∈Ω,0tT,u(x,0)=u0(x)0,x ∈,w(x,0)=w0(x)0,x ∈,It is shown that the solution to the problem exists globally if b+β≥0 and will blow up or quench if b+β0 by means of function transformation and comparison method.Various asymptotic behavior related to different coefficients and initial data is also discussed.