Slow-fast dynamics in a model of population and resource growth

Models of the interaction of population, the economy, and the environment often contain nonlinear functional relationships and variables that move at different speeds. These properties foster apparent unpredictabilities in system behaviour. Using a simple deterministic model of demographic, economic and environmental interactions we illustrate the usefulness of geometric singular perturbation theory in environmental population economics. In contrast to local stability analysis, the theory of slow-fast dynamics helps to gain new insights into the global behaviour of the system. In particular, the knowledge of the basins of attraction of the stationary states enables one to determine the regions of sustainable future paths of resources and population.