Interplay Between Synaptic Delays and Propagation Delays in Neural Field Equations

DOI10.1137/120889253zbMath1284.34116OpenAlexW1974562181MaRDI QIDQ2871372

Romain Veltz

Publication date: 22 January 2014

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/120889253

zbMATH Keywords

toruscenter manifoldequivariantbifurcation theoryfunctional differential equationswaveneural field equationsHopf-Hopf interactionspace-dependent delayspropagation delaysmixed-mode solutionnonuniform delay

Mathematics Subject Classification ID

Neural biology (92C20) Neural networks for/in biological studies, artificial life and related topics (92B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Functional-differential equations in abstract spaces (34K30) Stability theory of functional-differential equations (34K20) Integral operators (45P05) Systems of nonlinear integral equations (45G15) Bifurcation theory of functional-differential equations (34K18) Spectral theory; eigenvalue problems on manifolds (58C40) Invariant manifolds of functional-differential equations (34K19)

Related Items (8)

On the effects on cortical spontaneous activity of the symmetries of the network of pinwheels in visual area V1 ⋮ Pitchfork-Hopf bifurcations in 1D neural field models with transmission delays ⋮ Stability and bifurcations in Wilson-Cowan systems with distributed delays, and an application to basal ganglia interactions ⋮ On the stability of two neuron populations interacting with each other ⋮ The role of network structure and time delay in a metapopulation Wilson-Cowan model ⋮ Dynamics of delayed neural field models in two-dimensional spatial domains ⋮ Unnamed Item ⋮ Delay stabilizes stochastic motion of bumps in layered neural fields

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• dde23

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