Localised structures in nonlocal neural field models

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• Daniele Avitabile (Nottingham)
• Thursday 19 February 2015, 16:00-17:00
• Poynting Small Lecture Theatre.

If you have a question about this talk, please contact Alexandra Tzella.

I will discuss the formation of stationary localised solutions in 1D and 2D integral neural field models. First, a 1D inhomogeneous synaptic kernel with Heaviside firing rate will be considered. In this case, interface methods allow for the explicit construction of a bifurcation equation for localised steady states, so that analytical expressions for snakes and ladders can be derived. Similarly, eigenvalue computations can be carried out analytically to determine the stability of the solution profiles. I will then discuss a 2D model with homogeneous synaptic kernel that does not admit an equivalent PDE formulation. In this (and other neural field models featuring a convolution structure) it is advantageous to combine FFT and Newton-Krylov solvers to perform numerical bifurcation analysis directly on the integral model. I will present numerical results that show how the choice of synaptic kernel affects the bifurcation structure.

This talk is part of the Applied Mathematics Seminar Series series.

This talk is included in these lists:

• Applied Mathematics Seminar Series
• Poynting Small Lecture Theatre
• School of Mathematics Events

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