The link between integral equations and higher order ODEs.

DOI10.1016/J.JMAA.2003.10.023zbMath1041.45005OpenAlexW1991170894MaRDI QIDQ1426072

Edward P. Krisner

Publication date: 14 March 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2003.10.023

zbMATH Keywords

integral equationGreen's functioncouplinglateral inhibitionneural biologyhigher order ordinary differential equation

Mathematics Subject Classification ID

Neural biology (92C20) Green's functions for ordinary differential equations (34B27) Singular nonlinear integral equations (45G05)

Related Items (9)

Waves, bumps, and patterns in neural field theories ⋮ Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity ⋮ A gradient flow generated by a nonlocal model of a neural field in an unbounded domain ⋮ Existence and upper semicontinuity of global attractors for neural network in a bounded domain ⋮ Iterative schemes for bump solutions in a neural field model ⋮ Wave Phenomena in Neuronal Networks ⋮ Lower semicontinuity of global attractors for a class of evolution equations of neural fields type in a bounded domain ⋮ Asymptotic behavior of neural fields in an unbounded domain ⋮ Existence and stability of periodic solutions in a neural field equation

Cites Work

• Unnamed Item
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Existence and stability of local excitations in homogeneous neural fields
• Waves and bumps in neuronal networks with axo-dendritic synaptic interactions
• Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses
• Spatially Structured Activity in Synaptically Coupled Neuronal Networks: II. Lateral Inhibition and Standing Pulses
• Multiple Bumps in a Neuronal Model of Working Memory
• Existence and uniqueness of travelling waves for a neural network
• PDE Methods for Nonlocal Models
• Traveling fronts and wave propagation failure in an inhomogeneous neural network

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