Stability of non-autonomous population models with bounded and periodic enforcement.

The paper presents theorems on the global asymptotic behaviour of non-autonomous population models which for the special case of periodically forced populations generalize known results. It is shown that a non-autonomous discrete dynamical system on an interval possesses the property of path stability, if the system is given by cave functions. From this it follows for a periodic system with strictly cave functions that there exists a globally asymptotically stable cycle. Old and new examples are discussed. [ABSTRACT FROM AUTHOR]