Single bumps in a 2-population homogenized neuronal network model

DOI10.1016/J.PHYSD.2018.01.004zbMath1390.92013OpenAlexW2783827706MaRDI QIDQ1640898

Karina Kolodina, Anna Oleynik, John A. Wyller

Publication date: 14 June 2018

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

Full work available at URL: https://doi.org/10.1016/j.physd.2018.01.004

zbMATH Keywords

homogenization theoryneural field modelsexistence and stability of bumps

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Neural networks for/in biological studies, artificial life and related topics (92B20) Growth and boundedness of solutions to ordinary differential equations (34C11) Stability theory for integral equations (45M10)

Related Items (1)

Pattern formation in a 2-population homogenized neuronal network model

Cites Work

• Unnamed Item
• Unnamed Item
• Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity
• Waves in random neural media
• On the properties of nonlinear nonlocal operators arising in neural field models
• Wave fronts in inhomogeneous neural field models
• Some theoretical and numerical results for delayed neural field equations
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Spatially periodic modulation of cortical patterns by long-range horizontal connections
• Numerical analysis of bump solutions for neural field equations with periodic microstructure
• Homogenization of a Wilson-Cowan model for neural fields
• Snakes and ladders in an inhomogeneous neural field model
• Waves, bumps, and patterns in neural field theories
• Two bump solutions of a homogenized Wilson-Cowan model with periodic microstructure
• Localized activity patterns in two-population neuronal networks
• Spatiotemporal dynamics of continuum neural fields
• Towards a two-scale calculus
• EVANS FUNCTIONS AND NONLINEAR STABILITY OF TRAVELING WAVES IN NEURONAL NETWORK MODELS
• An Introduction to Fronts in Random Media
• 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
• Traveling Pulses and Wave Propagation Failure in Inhomogeneous Neural Media
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Front Propagation in Heterogeneous Media
• Breathing Pulses in an Excitatory Neural Network
• Bifurcations of Stationary Solutions in an Interacting Pair of E-I Neural Fields
• Heaviside World: Excitation and Self-Organization of Neural Fields
• A one-population Amari model with periodic microstructure
• Stimulus-Locked Traveling Waves and Breathers in an Excitatory Neural Network
• Spectral Stability of Vortices in Two-Dimensional Bose–Einstein Condensates via the Evans Function and Krein Signature
• Traveling fronts and wave propagation failure in an inhomogeneous neural network

This page was built for publication: Single bumps in a 2-population homogenized neuronal network model