Neural field models with transmission delays and diffusion
DOI10.1186/S13408-020-00098-5zbMath1475.92020arXiv1912.09762OpenAlexW2996507699WikidataQ104138842 ScholiaQ104138842MaRDI QIDQ2040388
Stephan A. van Gils, Yuri A. Kuznetsov, Len Spek
Publication date: 14 July 2021
Published in: The Journal of Mathematical Neuroscience (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.09762
Hopf bifurcationnormal formdelay equationneural fieldsun-star calculusnumerical bifurcation analysis
Neural networks for/in biological studies, artificial life and related topics (92B20) Numerical bifurcation problems (65P30) Bifurcation theory of functional-differential equations (34K18)
Related Items (1)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Local excitation-lateral inhibition interaction yields oscillatory instabilities in nonlocally interacting systems involving finite propagation delay
- Analysis of nonlocal neural fields for both general and gamma-distributed connectivities
- How effective delays shape oscillatory dynamics in neuronal networks
- Reflexivity, the dual Radon-Nikodym property, and continuity of adjoint semigroups
- Some theoretical and numerical results for delayed neural field equations
- On semilinear Cauchy problems with non-dense domain
- Mathematical foundations of neuroscience
- A simple global characterization for normal forms of singular vector fields
- The brain wave equation: A model for the EEG
- Dynamics of pattern formation in lateral-inhibition type neural fields
- Pitchfork-Hopf bifurcations in 1D neural field models with transmission delays
- Standing and travelling waves in a spherical brain model: the Nunez model revisited
- Perturbation theory for linear operators.
- Functional differential equations and nonlinear semigroups in \(L^p\) spaces
- Delay equations. Functional-, complex-, and nonlinear analysis
- Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
- Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
- Stability of the stationary solutions of neural field equations with propagation delays
- On local bifurcations in neural field models with transmission delays
- Waves, bumps, and patterns in neural field theories
- Normal forms for semilinear equations with non-dense domain with applications to age structured models
- Projectors on the generalized eigenspaces for functional differential equations using integrated semigroups
- Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay
- Dynamic instabilities in scalar neural field equations with space-dependent delays
- A Center Manifold Result for Delayed Neural Fields Equations
- Nonoscillation Theory of Functional Differential Equations with Applications
- A general bilinear vector integral
- Amplitude Equations for Systems with Competing Instabilities
- Exact Neural Fields Incorporating Gap Junctions
- Delays in activity-based neural networks
- Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations
- Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models
- Large Scale Spatially Organized Activity in Neural Nets
- One-Parameter Semigroups for Linear Evolution Equations
- A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
- ERRATUM: A Center Manifold Result for Delayed Neural Fields Equations
- Neural Fields
- Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
- Über die Stieltjessche Integration abstrakter Funktionen
- Elements of applied bifurcation theory
- Functional differential equations
- Semigroups and linear partial differential equations with delay
This page was built for publication: Neural field models with transmission delays and diffusion