Attractor minimal sets for cooperative and strongly convex delay differential systems

We study the skew-product semiflow induced by a family of convex and cooperative delay differential systems. Under some monotonicity assumptions, we obtain an ergodic representation for the upper Lyapunov exponent of a minimal subset. In addition, when eventually strong convexity at one point is assumed and there exist two completely strongly ordered minimal subsets K1 CK2, we show that K1 is an attractor subset which is a copy of the base. The long-time behaviour of every trajectory strongly ordered with K2 is then deduced. Some examples of application of the theory are shown.