Stationary solutions of continuous and discontinuous neural field equations

DOI10.1016/j.jmaa.2016.06.021zbMath1344.47053OpenAlexW2444318397MaRDI QIDQ530306

Evgenii Burlakov, Arcady Ponosov, John A. Wyller

Publication date: 29 July 2016

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.2016.06.021

zbMATH Keywords

solvabilitycontinuous dependencediscontinuous Hammerstein equations

Mathematics Subject Classification ID

Neural biology (92C20) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Applications of operator theory to differential and integral equations (47N20) Applications of operator theory in chemistry and life sciences (47N60) Integro-partial differential equations (35R09)

Related Items (7)

Pattern formation in a 2-population homogenized neuronal network model ⋮ Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity ⋮ On ring solutions of neural field equations ⋮ Multistability, scattering and selection of equilibria in the mechanical system with constraint ⋮ On continuous and discontinuous models of neural fields ⋮ On inclusions arising in neural field modeling ⋮ Existence and stability of periodic solutions in a neural field equation

Cites Work

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• Waves in random neural media
• On the properties of nonlinear nonlocal operators arising in neural field models
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Existence and stability of local excitations in homogeneous neural fields
• Numerical analysis of bump solutions for neural field equations with periodic microstructure
• Two-bump solutions of Amari-type models of neuronal pattern formation
• Homogenization of a Wilson-Cowan model for neural fields
• On the existence of unstable bumps in neural networks
• Two-dimensional Amari neural field model with periodic microstructure: rotationally symmetric bump solutions
• Iterative schemes for bump solutions in a neural field model
• Two bump solutions of a homogenized Wilson-Cowan model with periodic microstructure
• Spatiotemporal dynamics of continuum neural fields
• On wellposedness of generalized neural field equations with delay
• Existence and properties of solutions for neural field equations
• Persistent Neural States: Stationary Localized Activity Patterns in Nonlinear Continuous n-Population, q-Dimensional Neural Networks
• Evans Functions for Integral Neural Field Equations with Heaviside Firing Rate Function
• Spiking Neuron Models
• A one-population Amari model with periodic microstructure
• Neural networks and physical systems with emergent collective computational abilities.
• The Leray-Schauder index and the fixed point theory for arbitrary ANRs
• Applications of functional analysis and operator theory

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