Global attractivity of the zero solution to a Lotka-Volterra-type functional-differential equation (Q2749015)

The authors investigate the global attractivity of the zero solution to the Lotka-Volterra-type functional-differential equation NEWLINE\[NEWLINE x'(t)+[1+x(t)]F(t,1+\lambda x(\cdot))x(\cdot))=0,\quad t\geq 0,NEWLINE\]NEWLINE where \(F\) satisfies the Yorke condition and \(0\leq \lambda \leq 1\). They obtain the \(\frac{3}{2}\)-stability result and show that when this result will be applied to the single species model NEWLINE\[NEWLINEN'(t)=N(t)[a-bN(t-\tau)-cN^2(t-\tau)],\quad t\geq 0,NEWLINE\]NEWLINE then some known results are improved.