Evans Functions for Integral Neural Field Equations with Heaviside Firing Rate Function

@article{Coombes2004EvansFF,
  title={Evans Functions for Integral Neural Field Equations with Heaviside Firing Rate Function},
  author={Stephen Coombes and Markus R. Owen},
  journal={SIAM J. Applied Dynamical Systems},
  year={2004},
  volume={3},
  pages={574-600}
}
In this paper we show how to construct the Evans function for traveling wave solutions of integral neural field equations when the firing rate function is a Heaviside. This allows a discussion of wave stability and bifurcation as a function of system parameters, including the speed and strength of synaptic coupling and the speed of axonal signals. The theory is illustrated with the construction and stability analysis of front solutions to a scalar neural field model and a limiting case is shown… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 82 CITATIONS, ESTIMATED 21% COVERAGE

Traveling wave solutions to a neural field model with oscillatory synaptic coupling types.

  • Mathematical biosciences and engineering : MBE
  • 2019
VIEW 4 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Evans Functions and Nonlinear Stability of Traveling Waves in Neuronal Network Models

  • I. J. Bifurcation and Chaos
  • 2007
VIEW 16 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Threshold of Front Propagation in Neural Fields: An Interface Dynamics Approach

  • SIAM Journal of Applied Mathematics
  • 2018
VIEW 6 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Stochastic neural field models of binocular rivalry waves

VIEW 8 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Spatiotemporal dynamics of continuum neural fields

VIEW 10 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Neural fields with sigmoidal firing rates: Approximate solutions

VIEW 15 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Waves, bumps, and patterns in neural field theories

  • Biological Cybernetics
  • 2005
VIEW 8 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Hallucinogen persisting perception disorder in neuronal networks with adaptation

  • Journal of Computational Neuroscience
  • 2011
VIEW 7 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

FILTER CITATIONS BY YEAR

2005
2019

CITATION STATISTICS

  • 12 Highly Influenced Citations

  • Averaged 4 Citations per year over the last 3 years

References

Publications referenced by this paper.

Similar Papers

Loading similar papers…