Geometric analysis of ecological models with slow and fast processes

The interaction of fast and slow processes is an integral parr of the sudde n 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 bifu rcations in the dynamics of the fast components are at the heart of such dr amatic shifts. We discuss some of the most important bifurcations and show how they can be analyzed. Subsequently, we show how the interaction with sl owly changing variables can be understood from graphs constructed in a simp le way using the singular perturbation approach.