Stability and attractivity for Nicholson systems with time-dependent delays

We analyse the stability and attractivity of a class of $n$-dimensional Nicholson systems with constant coefficients and multiple time-varying delays. Delay-independent sufficient conditions on the coefficients are given, for the existence and absolute global exponential stability of a unique positive equilibrium $N^*$, generalizing and improving known results for autonomous systems. We further establish delay-dependent criteria for $N^*$ to be a global attractor of all positive solutions. In the latter case, upper bounds on the size of the delays which do not require an a priori explicit knowledge of the equilibrium $N^*$ are also derived.