On the properties of nonlinear nonlocal operators arising in neural field models

DOI10.1016/j.jmaa.2012.08.063zbMath1320.35354OpenAlexW2083349325MaRDI QIDQ691838

Anna Oleynik, Arcady Ponosov, John A. Wyller

Publication date: 4 December 2012

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.2012.08.063

zbMATH Keywords

Sobolev spacesnonlinear integral equationsdegree theorycontinuous dependenceneural field

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Neural networks for/in biological studies, artificial life and related topics (92B20) Integro-partial differential equations (35R09)

Related Items (12)

Pattern formation in a 2-population homogenized neuronal network model ⋮ On properties of solutions to differential systems modeling the electrical activity of the brain ⋮ Single bumps in a 2-population homogenized neuronal network model ⋮ Numerical analysis of bump solutions for neural field equations with periodic microstructure ⋮ Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity ⋮ On ring solutions of neural field equations ⋮ Two bump solutions of a homogenized Wilson-Cowan model with periodic microstructure ⋮ On continuous and discontinuous models of neural fields ⋮ Stationary solutions of continuous and discontinuous neural field equations ⋮ Regularization of ill-posed point neuron models ⋮ On inclusions arising in neural field modeling ⋮ Existence and stability of periodic solutions in a neural field equation

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