Stability in a class of discrete time models of interacting populations.

Effective Lyapunov and Lyapunov-like functions for a class of discrete time models of interacting populations are presented. These functions are constructed on the biologically meaningful principle that a viable population must absorb energy from external sources when its density is low and it must dissipate energy to the environment when its density is high. These functions can be used to establish that a discrete time model is globally stable or that its solutions are ultimately confined to an acceptable region of the state space. The latter is especially interesting when the model has chaotic solutions. These methods are applied to a single species model and a model of competition between two species.