Population Dynamics: General Insights from Local Analysis
Thilo Gross
Der Andere Verlag, 2004
In this thesis a new approach to the formulation and analysis of general models is presented. In general models the interaction between state variables is not restricted to specific functional forms. Instead they are described by general functions. This approach is used to formulate and study models of general food chains and food webs. This work illustrates that general models can be analysed in the framework of local bifurcation theory. In order to compute bifurcations efficiently a mathematical technique, the method of resultants, is derived. Application of the method of resultants and the general modelling approach reveals a new, general solution to the famous paradox of enrichment. Furthermore, the investigation of general models prove that chaotic parameter regions generally exist in systems with more than three trophic levels. The investigation of ecological food webs shows that a large class of food webs behaves qualitatively similar to food chains. Finally, it is shown that the strong form of the famous competitive-exclusion principle only occurs because of certain degeneracies that exist in simple ecological models.