Identification of a free energy functional in an integro-differential equation model for neuronal network activity.

DOI10.1016/j.aml.2004.07.007zbMath1070.45008OpenAlexW2060983374WikidataQ115360994 ScholiaQ115360994MaRDI QIDQ1767171

Donald A. French

Publication date: 7 March 2005

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2004.07.007

zbMATH Keywords

inverse problemcritical pointsenergy functionalsneuronal networksintegrodifferential convolution equation

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Neural networks for/in biological studies, artificial life and related topics (92B20) Inverse problems for integral equations (45Q05)

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Asymptotic behavior for a nonlocal model of neural fields ⋮ A gradient flow generated by a nonlocal model of a neural field in an unbounded domain ⋮ Interface dynamics in planar neural field models ⋮ Cortical-inspired Wilson-Cowan-type equations for orientation-dependent contrast perception modelling ⋮ Asymptotic behavior of neural fields in an unbounded domain ⋮ A dynamic neural field model of continuous input integration

Cites Work

• Unnamed Item
• Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity
• The computational modeling of nonequilibrium thermodynamics of the martensitic transformations
• An integrodifferential model for phase transitions: stationary solutions in higher space dimensions
• Stationary Bumps in Networks of Spiking Neurons
• 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
• Asymptotic behavior of solution to the Cahn-Hillard equation
• PDE Methods for Nonlocal Models
• Neurons with graded response have collective computational properties like those of two-state neurons.

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