具无界时滞非自治平方Logistic模型的全局吸引性

Global Attractivity in a Nonautonomous Square Logistic Model with Unbounded Delay

考虑非自治平方 L ogistic模型 Δxn=rnxn(1- bxn- kn- cxn- kn2 ) ,n=0 ,1,2… ,其中 { rn}为非负实数列 ,b≥ 0 ,c>0 ,{ kn}是非负整数列 ,{ n- kn}非单调递减 ,且 limn→∞(n- kn) =∞ ,给出了保证其每一正解 { xn}满足 limn→∞xn=x的一族充分条件 (其中 x是正平衡点 ) 。

Consider the nonautonomous square logistic model Δx n=r nx n(1-bx n-k n -cx n-k n 2) n =0,1,2,…,where ｛r n｝ is a sequence of nonnegative real numbers; b≥0,c≥0,｛k n｝ is a sequence of nonnegative integers; ｛n-k n｝ is nondercreasing;lim n→∞(n-k n)=∞ .We obtain the sufficient conditions that guarantees every positive solution of the equation to tend to the positive equilibrium.Our results improve some recent results and solve an open research project.