Geometric Analysis of Ecological Models with Slow and Fast Processes

The interaction of fast and slow processes is an integral part of the sudden large shifts that sometimes occur in ecosystems. To study the effects of slow/fast variables on ecosystems, we used a range of examples from natural and exploited aquatic and terrestrial systems. So-called catastrophic bifurcations in the dynamics of the fast components are at the heart of such dramatic shifts. We discuss some of the most important bifurcations and show how they can be analyzed. Subsequently, we show how the interaction with slowly changing variables can be understood from graphs constructed in a simple way using the singular perturbation approach. Received 30 November 1999; accepted 30 May 2000.