1. Numerical continuation of equilibria of physiologically structured population models. I
- Author
-
Ben Sommeijer, Odo Diekmann, Margreet Nool, Kirkilionis, A. de Roos, Bert Lisser, and Theoretical Ecology (IBED, FNWI)
- Subjects
Continuation ,Numerical continuation ,Population model ,Applied Mathematics ,Modeling and Simulation ,Numerical analysis ,Ordinary differential equation ,Mathematical analysis ,Applied mathematics ,Stability (probability) ,Integral equation ,Numerical stability ,Mathematics - Abstract
The paper introduces a new numerical method for continuation of equilibria of models describing physiologically structured populations. To describe such populations, we use integral equations coupled with each other via interaction (or feedback) variables. Additionally we allow interaction with unstructured populations, described by ordinary differential equations. The interaction variables are chosen such that if they are given functions of time, each of the resulting decoupled equations becomes linear. Our numerical procedure to approximate an equilibrium which will use this special form of the underlying equations extensively. We also establish a method for local stability analysis of equilibria in dependence on parameters.
- Published
- 2001