One item in ecology is how it is possible that ecosystems, large food webs, can persist. Previous studies have always focused on small food chains (Rosenzweig) or small food webs (May). Results from these studies have led to the believe that larger and more complex food webs or food chains are, in general, instable.
In this project larger food webs will be studied through bifurcation analysis
applied to ODE-systems used to describe the dynamical behaviour of these food
webs. Contrary to the more popular models these systems explicitly describe the
nutrients the producers feed on, while also taking into account mass conservation. The aim of this project is to gain an overview of the most important local bifurcations in ecosystem models. Also, there is a focus on global bifurcations, such as homoclinic orbits and the Shil'nikov bifurcation.
In the models, based on Dynamic Energy Budget theory, it is assumed that populations live in an open environment, a chemostat. The programs AUTO, Content and LOCBIF are used to apply bifurcation analysis to analyze numerically the dynamical behaviour of these models. Case studies involving different kinds of interactions or trophic levels (omnivory, symbiosis, multiple resources, pathogens) will be made in this projects to gain insight into the behaviour of large scale ecosystems.