Bifurcation Analysis in 1D diffusive neural fields models with transmission delays

Abstract

Bifurcation theory for delay differential equations on neural field models has been extensively analysed in the paper of Stephan van Gils et al. Shortly after, in the paper of Koen Dijkstra et al., it was shown how symmetry arguments could simplify the computation of the spectrum and of the normal forms. In this thesis spatial diffusion has been incorporated in the delayed neural field equation. A bifurcation analysis on known examples is carried forward and the influence of the diffusion coefficient on both the spectrum and the normal form coefficients are analysed.