Intrinsic excitability and the role of saddle slow manifolds

Datum

19.08.2016

Zeit

10:00 - 11:00

Sprecher

Prof. Dr. Hinke Osinga

Zugehörigkeit

University of Auckland, Dept. of Mathematics

Serie

TUD Mathematik Oberseminar Analysis

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Prof. Dr. S. Siegmund

Beschreibung

: Excitable cells, such as neurons, exhibit complex oscillations in response to external input, e.g., from other neurons in a network. We consider the effect of a brief stimulation from the rest state of a minimal neuronal model with multiple time scales. The transient dynamics arising from such short current injections brings out the intrinsic bursting capabilities of the system. We focus on transient bursts, that is, the transient generation of one or more spikes, and use a simple polynomial model to illustrate our analysis. We take a geometric approach to explain how spikes arise and how their number changes as parameters are varied. We discuss how the onset of new spikes is controlled by stable manifolds of a slow manifold of saddle type. We give a precise definition of such a stable manifold and use numerical continuation of suitable two-point boundary value problems to approximate them. This is joint work with Krasimira Tsaneva-Atanasova (University of Exeter), Vivien Kirk and Saeed Farjami (both University of Auckland).

Links

• Oberseminar Analysis

Letztmalig verändert: 03.08.2016, 16:13:42