Abstract
In this paper we derive some criteria of global attraction to a positive equilibrium for the equation
x'(t) = -beta x(t) + beta F(x(t - sigma), x(t - tau)),
where 0 <= sigma tau, beta > 0, and F : [0, infinity)(2) -> [0, infinity) is a smooth map. The method of proof is reminiscent to the classical approach of "decomposing +embedding". Our results have two strengths: (i) We derive delay-dependent conditions of global attraction. (ii) We impose monotonicity conditions only on the second variable of F.