Feedback control systems analysis of density dependent population dynamics

We use feedback control methods to prove existence of globally asymptotically stable equilibria for nonlinear (density dependent) population dynamics. We focus on populations modelled in discrete size or stage classes so that the model has a natural state space of nonnegative vectors in R. Combining comparison results and small gain techniques, we characterize the situations when there is a positive (in the sense of cones) globally asymptotically stable equilibrium, situations when zero is globally asymptotically stable, and situations when all solutions with non-zero initial conditions diverge. We apply our results to a model of Chinook Salmon.