Global attractivity of a logistic model with unbounded delay (Q2748226)

The authors consider the logistic model with unbounded delay, NEWLINE\[NEWLINE\Delta x_n=r_n x_n\left(1-{x_n- k_n\over K}\right),\;n=0,1,2,\dots,NEWLINE\]NEWLINE where \(\{r_n\}^\infty_{n=0}\) is a sequence of non-negative real numbers, \(\{k_n \}\) is a sequence of non-negative integers satisfying \(\lim_{n \to\infty} (n-k_n)= \infty\), \(\limsup_{n \to\infty} k_n= \infty\), and \(K\) is a positive constant.NEWLINENEWLINENEWLINEObviously, \(K\) is the unique positive equilibrium point of the logistic model. They investigate the global attractivity of the positive equilibrium \(K\) (Theorem 1) and they give a new sufficient condition, which improves some known results.