Population dynamics: general results from local analysis

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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Oldenburg

Year

2004

Author dc:creator

• Groß, Thilo

• [Keine Schlagwörter von Autor/in vergeben.]

Repository record source_url

http://oops.uni-oldenburg.de/180

OAI identifier oai:identifier

oai:oops.uni-oldenburg.de:180