A note on traveling fronts and pulses in a firing rate model of a neuronal network

DOI10.1016/j.physd.2004.06.005zbMath1049.92008OpenAlexW2002098235MaRDI QIDQ1881726

M. Enculescu

Publication date: 14 October 2004

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2004.06.005

zbMATH Keywords

Traveling wavesNeuronal networksConvolution equations

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Neural biology (92C20) Neural networks for/in biological studies, artificial life and related topics (92B20) Numerical methods for integral equations, integral transforms (65R99)

Related Items

Wave fronts in inhomogeneous neural field models, Waves, bumps, and patterns in neural field theories, Existence and nonexistence of traveling pulses in a lateral inhibition neural network, Speeds of traveling waves in some integro-differential equations arising from neuronal networks, Influence of sodium currents on speeds of traveling wave fronts in synaptically coupled neuronal networks, Stabilization of pulse waves through inhibition in a feedforward neural network, Travelling wave solutions of integro-differential equations of one-dimensional neuronal networks

Cites Work

• Dynamics of pattern formation in lateral-inhibition type neural fields
• A mathematical theory of visual hallucination patterns
• The analysis of synaptically generated traveling waves
• Waves and bumps in neuronal networks with axo-dendritic synaptic interactions
• Multiple-spike waves in a one-dimensional integrate-and-fire neural network
• PDE Methods for Nonlocal Models
• Effects of delay on the type and velocity of travelling pulses in neuronal networks with spatially decaying connectivity
• A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
• Traveling fronts and wave propagation failure in an inhomogeneous neural network