The weakly nonlocal limit of a one-population Wilson-Cowan model

DOI10.1016/j.physd.2010.05.011zbMath1254.92014OpenAlexW2019727141WikidataQ125337021 ScholiaQ125337021MaRDI QIDQ1957118

Anna Oleynik, John A. Wyller

Publication date: 24 September 2010

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

Full work available at URL: https://doi.org/10.1016/j.physd.2010.05.011

zbMATH Keywords

wavelet-Galerkin methodnonlocalneural field models

Mathematics Subject Classification ID

Neural biology (92C20) Dynamical systems in biology (37N25) Numerical problems in dynamical systems (65P99)

Uses Software

• XPPAUT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis of nonlocal neural fields for both general and gamma-distributed connectivities
• Turing instability and pattern formation in a two-population neuronal network model
• Exploiting the Hamiltonian structure of a neural field model
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Existence and stability of local excitations in homogeneous neural fields
• Wavelet-Galerkin method for integro-differential equations
• Waves, bumps, and patterns in neural field theories
• Localized activity patterns in two-population neuronal networks
• Dynamic instabilities in scalar neural field equations with space-dependent delays
• 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
• Simulating, Analyzing, and Animating Dynamical Systems
• Traveling Pulses and Wave Propagation Failure in Inhomogeneous Neural Media
• Orthonormal bases of compactly supported wavelets
• On the Representation of Operators in Bases of Compactly Supported Wavelets
• Introduction to Partial Differential Equations
• Wavelet–Galerkin solutions for one‐dimensional partial differential equations
• THE COMPUTATION OF WAVELET-GALERKIN APPROXIMATION ON A BOUNDED INTERVAL
• An introduction to synergetics
• Stability and Bifurcations in Neural Fields with Finite Propagation Speed and General Connectivity
• A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
• Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations
• Connection coefficients on an interval and wavelet solutions of Burgers equation

This page was built for publication: The weakly nonlocal limit of a one-population Wilson-Cowan model