广义时滞Logistic方程的全局吸收性

Global Attractivity in a Generalized Delay Logistic Equation

研究广义时滞Logistic方程N′(t) =r(t)N(t) (1-N(g(t) ) ) α,t 0 ,其中r(t) >0 ,g(t) ∈C([0 ,+∞ ) ,R) ,g(t) <t,limt→∞g(t) =+∞ ,α 1为两奇数之比 ,获得了方程每一正解N(t) 趋于 1的一族充分条件 ,改进了已有的相应结论 .

The following generalized delay Logistic equation is studiedN′(t)=r(t)N(t)(1-N(g(t))) α, t0,where r(t)>0, g(t)∈C([0,+∞),R),g(t)<t, lim[DD(X]t→∞g(t)=+∞,α1 a ratio of two odd integers. Some sufficient conditions under which every positive solution of the equation convergences to 1 as t tends to infinite are obtained. Some known results are improved.