Physiologically structured population models: Towards a general mathematical theory
Authors: Diekmann O, Gyllenberg M, Metz JAJ
Publication Year: 2007
Reference: In Mathematics for Ecology and Environmental Sciences, Y. Takeuchi, Y. Iwasa, K. Sato (eds)
Springer-Verlag, Berlin Heidelberg, Germany pp.5-20 (2007)
. Also available as IIASA Interim Report IR-07-046 www.iiasa.ac.at/Admin/PUB/Documents/IR-07-046.pdf
Abstract
We review the state-of-the-art concerning a mathematical framework for general physiologically structured population models. When individual development is affected by the population density, such models lead to quasilinear equations. We show how to associate a dynamical system (defined on an infinite dimensional state space) to the model and how to determine the steady states. Concerning the principle of linearized stability, we offer a conjecture as well as some preliminary steps towards a proof.