Numerical Simulations of SDEs and SPDEs From Neural Systems Using SDELab

Hasan Alzubaidi, Hagen Gilsing, Tony Shardlow

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (SciVal)

Abstract

Stochastic differential equations are an important class of models that allow for a time varying random forcing in standard deterministic differential equations. We introduce the Itô stochastic differential equation as a generalisation of the standard finite dimensional initial value problem for ODEs. The Hodgkin-Huxley model is given as an example. We also look at reaction-diffusion equations, in particular the FitzHugh-Nagumo model, under the influence of stochastic forcing. Examples are given in the computer environment MATLAB.

Original languageEnglish
Title of host publicationStochastic Methods in Neuroscience
PublisherOxford University Press
ISBN (Electronic)9780191715778
ISBN (Print)9780199235070
DOIs
Publication statusPublished - 1 Feb 2010

Keywords

  • FitzHugh-Nagumo
  • Hodgkin-Huxley
  • Initial value problem
  • Itô calculus
  • Stochastic differential equation
  • Stochastic PDEs

ASJC Scopus subject areas

  • Mathematics(all)

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