Cumulative Formulation of (Physiologically) Structured Population Models

摘要

It is argued that a formulation of structured population models in terms ofabstract renewal equations, combined with a feedback law, is at the same time natural, elegant, and technically advantageous compared to partial functional differential equations. General physiologically structured population models can be mathematically described by a renewal equation and a feedback law. The main advantage of such a formulation is that it avoids the use of unbounded operators (the generating family) for which a precise description of the domain of definition is a technically hard and unpleasant task, if possible at all. The plan is to use this formulation as the starting point for a qualitative theory for nonlinear problems, dealing in particular with stability and bifurcation.