scholarly journals Pitchfork–Hopf bifurcations in 1D neural field models with transmission delays

2015 ◽  
Vol 297 ◽  
pp. 88-101 ◽  
Author(s):  
K. Dijkstra ◽  
S.A. van Gils ◽  
S.G. Janssens ◽  
Yu.A. Kuznetsov ◽  
S. Visser
Keyword(s):  
Neural Field ◽  
Hopf Bifurcations ◽  
Transmission Delays ◽  
Neural Field Models

scholarly journals Neural field models with transmission delays and diffusion

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Len Spek ◽  
Yuri A. Kuznetsov ◽  
Stephan A. van Gils
Keyword(s):  
Large Scale ◽  
Neural Field ◽  
Diffusion Term ◽  
Transmission Delays ◽  
Neural Field Model ◽  
Lyapunov Coefficient ◽  
Electrical Connections ◽  
Large Groups ◽  
And Diffusion ◽  
Neural Field Models

AbstractA neural field models the large scale behaviour of large groups of neurons. We extend previous results for these models by including a diffusion term into the neural field, which models direct, electrical connections. We extend known and prove new sun-star calculus results for delay equations to be able to include diffusion and explicitly characterise the essential spectrum. For a certain class of connectivity functions in the neural field model, we are able to compute its spectral properties and the first Lyapunov coefficient of a Hopf bifurcation. By examining a numerical example, we find that the addition of diffusion suppresses non-synchronised steady-states while favouring synchronised oscillatory modes.

scholarly journals On local bifurcations in neural field models with transmission delays

2012 ◽  
Vol 66 (4-5) ◽  
pp. 837-887 ◽  
Author(s):  
S. A. van Gils ◽  
S. G. Janssens ◽  
Yu. A. Kuznetsov ◽  
S. Visser
Keyword(s):  
Neural Field ◽  
Transmission Delays ◽  
Local Bifurcations ◽  
Neural Field Models

Dynamic Approximation of Spatiotemporal Receptive Fields in Nonlinear Neural Field Models

2002 ◽  
Vol 14 (8) ◽  
pp. 1801-1825 ◽  
Author(s):  
Thomas Wennekers
Keyword(s):  
Order Approximation ◽  
Receptive Fields ◽  
Neural Field ◽  
Orientation Tuning ◽  
Field Equations ◽  
Dynamic Tuning ◽  
Dimensional Approximation ◽  
Low Dimensional ◽  
Spatiotemporal Response ◽  
Neural Field Models

This article presents an approximation method to reduce the spatiotemporal behavior of localized activation peaks (also called “bumps”) in nonlinear neural field equations to a set of coupled ordinary differential equations (ODEs) for only the amplitudes and tuning widths of these peaks. This enables a simplified analysis of steady-state receptive fields and their stability, as well as spatiotemporal point spread functions and dynamic tuning properties. A lowest-order approximation for peak amplitudes alone shows that much of the well-studied behavior of small neural systems (e.g., the Wilson-Cowan oscillator) should carry over to localized solutions in neural fields. Full spatiotemporal response profiles can further be reconstructed from this low-dimensional approximation. The method is applied to two standard neural field models: a one-layer model with difference-of-gaussians connectivity kernel and a two-layer excitatory-inhibitory network. Similar models have been previously employed in numerical studies addressing orientation tuning of cortical simple cells. Explicit formulas for tuning properties, instabilities, and oscillation frequencies are given, and exemplary spatiotemporal response functions, reconstructed from the low-dimensional approximation, are compared with full network simulations.

scholarly journals Neural field models for latent state inference: Application to large-scale neuronal recordings

2019 ◽  
Vol 15 (11) ◽  
pp. e1007442
Author(s):  
Michael E. Rule ◽  
David Schnoerr ◽  
Matthias H. Hennig ◽  
Guido Sanguinetti
Keyword(s):  
Large Scale ◽  
Neural Field ◽  
State Inference ◽  
Neural Field Models

scholarly journals On conductance-based neural field models

2013 ◽  
Vol 7 ◽  
Author(s):  
Dimitris A. Pinotsis ◽  
Marco Leite ◽  
Karl J. Friston
Keyword(s):  
Neural Field ◽  
Neural Field Models
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