A gradient flow formulation for the stochastic Amari neural field model
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Publication:2330609
DOI10.1007/s00285-019-01393-wzbMath1423.60102arXiv1807.02575OpenAlexW2816358064WikidataQ92865873 ScholiaQ92865873MaRDI QIDQ2330609
Christian Kuehn, Jonas M. Tölle
Publication date: 22 October 2019
Published in: Journal of Mathematical Biology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1807.02575
nonnegative kernelgradient flow in nonlocal Hilbert spacespace-time regularity of solutionsspatially correlated additive noisestochastic Amari neural field equationunique invariant measure of the ergodic Feller semigroup
Smoothness and regularity of solutions to PDEs (35B65) Neural biology (92C20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Nonlocal and multipoint boundary value problems for ordinary differential equations (34B10)
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Cites Work
- Unnamed Item
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- A nonlocal continuum model for biological aggregation
- Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers law and beyond
- Existence and uniqueness of invariant measures for stochastic evolution equations with weakly dissipative drifts
- Wavelet kernel principal component analysis in noisy multiscale data classification
- On bounded positive stationary solutions for a nonlocal Fisher-KPP equation
- Stochastic partial differential equations: an introduction
- An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two
- A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs
- Eigenvalues of integral operators defined by smooth positive definite kernels
- On the nuclearity of integral operators
- Non-monotone stochastic generalized porous media equations
- Positive definite functions and generalizations, an historical survey
- Dynamics of pattern formation in lateral-inhibition type neural fields
- Parabolic Ito equations with monotone nonlinearities
- A non-local model for a swarm
- Attractors for random dynamical systems
- A gradient flow generated by a nonlocal model of a neural field in an unbounded domain
- Well-posedness of the stochastic neural field equation with discontinuous firing rate
- Multivariate characteristic and correlation functions
- Positive definiteness, reproducing kernel Hilbert spaces and beyond
- Laws of large numbers and Langevin approximations for stochastic neural field equations
- Large deviations for nonlocal stochastic neural fields
- Sharp asymptotics of metastable transition times for one dimensional SPDEs
- Stochastic neural field equations: a rigorous footing
- Waves, bumps, and patterns in neural field theories
- Stochastic generalized porous media and fast diffusion equations
- Invariant measures for semilinear SPDE's with local Lipschitz drift coefficients and applications
- Invariant measures for monotone SPDEs with multiplicative noise term
- Multi-valued, singular stochastic evolution inclusions
- Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
- Ergodicity for nonlinear stochastic equations in variational formulation
- A note on semilinear stochastic equations
- Zur Umkehrbarkeit der statistischen Naturgesetze
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- A General Framework for Stochastic Traveling Waves and Patterns, with Application to Neural Field Equations
- A Multiscale Analysis of Traveling Waves in Stochastic Neural Fields
- Wandering Bumps in Stochastic Neural Fields
- Front Propagation in Stochastic Neural Fields
- Front Propagation in Stochastic Neural Fields: A Rigorous Mathematical Framework
- Kramers' law: Validity, derivations and generalisations
- Stochastic Neural Field Theory and the System-Size Expansion
- Spatiotemporal dynamics of continuum neural fields
- The effects of noise on binocular rivalry waves: a stochastic neural field model
- Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations
- The non-local Fisher–KPP equation: travelling waves and steady states
- Parabolic Ito Equations
- Semilinear stochastic equations for symmetric diffusions
- The Variational Formulation of the Fokker--Planck Equation
- PDE Methods for Nonlocal Models
- A meeting point of entropy and bifurcations in cross-diffusion herding
- A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
- Rate Models for Conductance-Based Cortical Neuronal Networks
- Ergodicity for Infinite Dimensional Systems
- Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation
- Stochastic Equations in Infinite Dimensions
- Stochastic Motion of Bumps in Planar Neural Fields
- Noise-Induced Behaviors in Neural Mean Field Dynamics
- Neural Fields
- Travelling front solutions of a nonlocal Fisher equation
- Nonlocal control of pulse propagation in excitable media
