The discrete dynamics of monotonically decomposable maps.

We extend results of Gouzé and Hadeler (in Nonlinear World 1:23-34, 1994) concerning the dynamics generated by a map on an ordered metric space that can be decomposed into increasing and decreasing parts. Our main results provide sufficient conditions for the existence of a globally asymptotically stable fixed point for the map. Applications to discrete-time, stage-structured population models are given.