Minisymposium: Endocrinologie mathématique en santé et médecine
Dynamical systems analysis of sustained and transient bursting oscillations in an endocrine cell model
Tsaneva-Atanasova, Krasimira (1) and Hinke Osinga (2)
(1) University of Bristol, UK, (2) University of Auckland, NZ

The models that describe endocrine cells bursting activity typically involve different time scales, but a standard bifurcation analysis of the fast time limit does not capture some phenomena. In particular termination of the active phase and spike adding are still not very well understood. Furthermore, dynamical systems tools are designed to explain the long-term bahaviour of a system, that is, what happens after transients have died out. In many situations, however, it may be important to understand the transient rather than sustained (asymptotic) behaviour. In this talk we employ standard tools from dynamical systems in order to analyse sustained and transient bursting behaviour. We show how manifolds of the fast subsystem are involved in the termination of the active phase and investigate these models further by performing bifurcation analysis of the full fast-slow system. We take a geometric approach to illustrate how the underlying fast subsystem organises the spike adding in much the same way as for spike adding in sustained periodic bursts, but the bifurcation analysis for spike onset is entirely different. Our results highlight the similarities between spike adding as a transient phenomenon and spike adding for periodic bursting, because the transients are organised by the same underlying geometric structure.

Mardi, 18 juin, 16h00
Salle Du Jardin