一类具有脉冲的时滞微分方程的全局吸引性

Global Attractivity of a Class of Delay Differential Equation with Impulsives

考虑具有脉冲的时滞微分方程:N′(t)=r(t)N(t)1-N(t-τ)1-λN(t-τ), t≥0,t≠tk,k∈N,lnN(t+k)-lnN(tk)=bklnN(tk), k∈N,( )其中,τ>0,λ∈(0,1),r∈C([0,+∞),R+),bk>-1,且{tk}满足0<t1<t2<…<tk<…,limt→∞tk=∞,给出了保证方程组( )的每一解N(t)满足limt→∞N(t)=1的一族充分条件.

Consider the impulsive delay differential equation:N′(t)=r(t)N(t)1-N(t-τ)1-λN(t-τ),t≥0, t≠tk, k∈N, lnN(t+k)-lnN(tk)=bklnN(tk),k∈N,(*)where: τ>0,λ∈(0,1),r∈C([0,+∞),R+),bk>-1, and {tk} satisfy 0<t1<t2<…<tk<…, limt→∞tk=∞. We obtain some sufficient conditions for every solution N(t) of the equation (*) satisfy limt→∞N(t)=1.