|
cgiet_01

Prof. Dr. Stephan van Gils (Twente University Enschede) On Local Bifurcations in Neural Field Models with Transmission Delays

Mittwoch, 03.07.2013 15:00 im Raum M5
Mathematik und Informatik

Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral properties, we elaborate extensively an example and derive a characteristic equation. Under certain conditions the associated equilibrium may destabilize in a Hopf bifurcation. Furthermore, two Hopf curves may intersect in a double Hopf point in a two-dimensional parameter space. We provide general formulas for the corresponding critical normal form coefficients, evaluate these numerically and interpret the results.



Angelegt am Mittwoch, 12.06.2013 14:53 von cgiet_01
Geändert am Mittwoch, 12.06.2013 15:06 von cgiet_01
[Edit | Vorlage]

Oberseminar Angewandte Mathematik
Sonstige Vorträge
Oberseminar zur Analysis