Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity

DOI10.1016/j.jde.2016.08.026zbMathNonearXiv1511.06364OpenAlexW2963471184MaRDI QIDQ324588

Vadim Kostrykin, Arcady Ponosov, Anna Oleynik, Alexander V. Sobolev

Publication date: 17 October 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.06364

zbMATH Keywords

nonlinear integral equationsFitzhugh-Nagumo modelbumpsneural field modelsigmoid type nonlinearities

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Neural networks for/in biological studies, artificial life and related topics (92B20) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Integral operators (47G10) Applications of operator theory in chemistry and life sciences (47N60) Theoretical approximation of solutions to integral equations (45L05)

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Pattern formation in a 2-population homogenized neuronal network model ⋮ Single bumps in a 2-population homogenized neuronal network model ⋮ Well-posedness of the stochastic neural field equation with discontinuous firing rate ⋮ On continuous and discontinuous models of neural fields ⋮ 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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