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Bifurcations in neural field models with transmission delays and diffusion

Spek, Len (2018) Bifurcations in neural field models with transmission delays and diffusion.

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Abstract:Neural Field Equations model the large scale behaviour of large groups of neurons. In this context gap junctions, electrical connections between neurons, are modelled by adding diffusion to the neural field. In this work we study the role of diffusion next to the usual connectivity with transmission delay. We extend known sun-star calculus results for delay equations to be able to include diffusion. Consequently, we are able to compute the spectral properties and normal form coefficients on the center manifold for Hopf and Pitchfork-Hopf bifurcations. By examining a numerical example, we find that the addition of diffusion suppresses spatial modes, while leaving temporal modes unaffected.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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