Numerical continuation of equilibria of physiologically structured population models. I. Theory

Citation
Ma. Kirkilionis et al., Numerical continuation of equilibria of physiologically structured population models. I. Theory, MATH MOD M, 11(6), 2001, pp. 1101-1127
Citations number
23
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
ISSN journal
02182025 → ACNP
Volume
11
Issue
6
Year of publication
2001
Pages
1101 - 1127
Database
ISI
SICI code
0218-2025(200108)11:6<1101:NCOEOP>2.0.ZU;2-O
Abstract
The paper introduces a new numerical method for continuation of equilibria of models describing physiologically structured populations. To describe su ch populations, we use integral equations coupled with each other via inter action (or feedback) variables. Additionally we allow interaction with unst ructured populations, described by ordinary differential equations. The int eraction variables are chosen such that if they are given functions of time , each of the resulting decoupled equations becomes linear. Our numerical p rocedure 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.