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Thursday, October 10, 2013

Local Bifurcations in Neural Field Equations

Yuri Kuznetsov (UU)

Abstract: 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, an example will be presented where the spectrum and the resolvent can be found explicitly. Under certain conditions the associated equilibrium may exhibit an Andronov-Hopf bifurcation that generates periodic oscillations. General formulas for the critical normal form coefficient are provided and evaluated numerically. The predicted bifurcation scenario is verified by simulations. Reference:S.A. van Gils, S.G. Janssens, Yu.A. Kuznetsov, and S. Visser. "On local bifurcations in neural field models with transmission delays" J. Math. Biol. 66 (2013) 837-887.

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Location :  Room 611 of the Hans Freudenthal building, formerly known as the Wiskunde/Maths building, (campus De Uithof) Budapestlaan 6, Utrecht.
Date and time : Thursday, October 10, 2013 15:30-16:30. The lecture is preceded by coffee, tea, and cookies from 15.00 to 15.30 hour in the same room.