Mathematical Biology Seminar

Seminar information archive ~07/24Next seminarFuture seminars 07/25~


15:00-16:20   Room #056 (Graduate School of Math. Sci. Bldg.)
Odo Diekmann (Mathematical Institute, Utrecht University)
The delay equation formulation of physiologically structured population models
[ Abstract ]
Traditionally, physiologically structured population models are formulated in terms of first order partial differential equations with non-local boundary conditions and/or transformed arguments. The stability and bifurcation theory for such equations is, in the quasi-linear case, still very immature.
The aim of this lecture is to explain that, alternatively, one can formulate such models in terms of delay equations (more precisely : renewal equations coupled to delay differential equations) without losing essential information and that for delay equations there is a well-developed local stability and bifurcation theory. As a motivating example we consider the interaction between a size-structured consumer and an unstructured resource. The lecture is based on joint work with Mats Gyllenberg and Hans Metz.