Analysis of Dynamics of Neural Fields and Neural Networks

Research output: ThesisPhD Thesis - Research UT, graduation UT

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Abstract

This thesis deals with the development and analysis of neural fields and neural networks. Neural fields model the averaged scale behaviour of large groups of neurons, where we include a transmission delay and a diffusion term modelling gap junctions. We investigate the dynamical behaviour of such models and study Hopf bifurcation with and without symmetry. We also expand the mathematical framework for delay equations, the sun-star calculus, to cover our model. Neural networks are used in machine learning to learn arbitrary mappings on some data set. We investigate these networks in a continuum limit using functional analysis and show how they fit in the reproducing kernel Banach spaces.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • University of Twente
Supervisors/Advisors
  • van Gils, Stephan A., Supervisor
  • Kuznetsov, Yu.A., Supervisor
  • Brune, Christoph, Co-Supervisor
Award date13 Jan 2023
Place of PublicationEnschede
Publisher
Print ISBNs978-90-365-5482-4
DOIs
Publication statusPublished - 13 Jan 2023

Keywords

  • Neural field
  • Neural network
  • functional analysis
  • Delay equation

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