Stochastic Partial Differential Equations in Neurobiology: Linear and Nonlinear Models for Spiking Neurons

DOI10.1007/978-3-642-32157-3_6zbMath1390.92034OpenAlexW118424158MaRDI QIDQ4567933

Henry C. Tuckwell

Publication date: 20 June 2018

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-32157-3_6

zbMATH Keywords

Ornstein-Uhlenbeck processesHodgkin-Huxley systemFitzHugh-Nagumo approximation

Mathematics Subject Classification ID

Neural biology (92C20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (10)

Mean field analysis of large-scale interacting populations of stochastic conductance-based spiking neurons using the Klimontovich method ⋮ Numerical Continuation and SPDE Stability for the 2D Cubic-Quintic Allen--Cahn Equation ⋮ Numerical solutions of some stochastic hyperbolic wave equations including sine-Gordon equation ⋮ Splitting schemes for FitzHugh-Nagumo stochastic partial differential equations ⋮ High-frequency analysis of parabolic stochastic PDEs ⋮ Parameter estimation for a linear parabolic SPDE model in two space dimensions with a small noise ⋮ Parameter estimation for SPDEs based on discrete observations in time and space ⋮ Volatility estimation for stochastic PDEs using high-frequency observations ⋮ Travelling waves in monostable and bistable stochastic partial differential equations ⋮ Multiscale analysis for traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations

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