Analysis and approximation of stochastic nerve axon equations

DOI10.1090/mcom/3068zbMath1342.60100arXiv1402.4791OpenAlexW3140363029MaRDI QIDQ2814447

Martin Sauer, Wilhelm Stannat

Publication date: 22 June 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.4791

zbMATH Keywords

stochastic reaction-diffusion equationsfinite difference approximationFitzHugh-Nagumo equationsHodgkin-Huxley equationsconductance based neuronal models

Mathematics Subject Classification ID

Neural biology (92C20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (10)

Numerical Continuation and SPDE Stability for the 2D Cubic-Quintic Allen--Cahn Equation ⋮ Enhancing the Order of the Milstein Scheme for Stochastic Partial Differential Equations with Commutative Noise ⋮ Splitting schemes for FitzHugh-Nagumo stochastic partial differential equations ⋮ Random attractors for stochastic partly dissipative systems ⋮ Forward invariance and Wong-Zakai approximation for stochastic moving boundary problems ⋮ Reliability of signal transmission in stochastic nerve axon equations ⋮ Drift estimation for stochastic reaction-diffusion systems ⋮ Travelling waves in monostable and bistable stochastic partial differential equations ⋮ Multiscale analysis for traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations ⋮ Stochastic rotating waves

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