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

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.