Numerical solution of the stochastic neural field equation with applications to working memory

DOI10.1016/J.PHYSA.2022.127166OpenAlexW4214841810MaRDI QIDQ2128715

Yanyan Li

Publication date: 22 April 2022

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

Full work available at URL: https://doi.org/10.1016/j.physa.2022.127166

zbMATH Keywords

Galerkin methodone- and multi-bump solutionsstochastic neural field equation

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Numerical methods for integral equations (65R20) Neural biology (92C20) Control/observation systems governed by functional-differential equations (93C23) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Applications to the sciences (65Z05) Stochastic integral equations (60H20) Numerical analysis (65-XX)

Cites Work

• Some theoretical and numerical results for delayed neural field equations
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Numerical simulation of stochastic PDEs for excitable media
• A dynamic neural field model of continuous input integration
• Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network
• Numerical solution of the neural field equation in the presence of random disturbance
• Large deviations for nonlocal stochastic neural fields
• Multi-bump solutions in a neural field model with external inputs
• Spatially Structured Activity in Synaptically Coupled Neuronal Networks: II. Lateral Inhibition and Standing Pulses
• Wandering Bumps in Stochastic Neural Fields
• Spatiotemporal dynamics of continuum neural fields
• Multiple Bumps in a Neuronal Model of Working Memory
• Numerical Solution of the Neural Field Equation in the Two-Dimensional Case
• EVANS FUNCTIONS AND NONLINEAR STABILITY OF TRAVELING WAVES IN NEURONAL NETWORK MODELS
• PDE Methods for Nonlocal Models
• Numerical Simulation Scheme of One- and Two Dimensional Neural Fields Involving Space-Dependent Delays
• Numerical Investigation of Stochastic Neural Field Equations
• Neural Fields
• Existence and Stability of Standing Pulses in Neural Networks: II. Stability

This page was built for publication: Numerical solution of the stochastic neural field equation with applications to working memory