Numerical Simulations of SDEs and SPDEs From Neural Systems Using SDELab

Hasan Alzubaidi; Hagen Gilsing; Tony Shardlow

doi:10.1093/acprof:oso/9780199235070.003.0012

Numerical Simulations of SDEs and SPDEs From Neural Systems Using SDELab

Hasan Alzubaidi, Hagen Gilsing, Tony Shardlow

Research output: Chapter or section in a book/report/conference proceeding › Book chapter

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 language	English
Title of host publication	Stochastic Methods in Neuroscience
Publisher	Oxford University Press
ISBN (Electronic)	9780191715778
ISBN (Print)	9780199235070
DOIs	https://doi.org/10.1093/acprof:oso/9780199235070.003.0012
Publication status	Published - 1 Feb 2010

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1093/acprof:oso/9780199235070.003.0012

Cite this

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title = "Numerical Simulations of SDEs and SPDEs From Neural Systems Using SDELab",

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 It{\^o} 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.",

keywords = "FitzHugh-Nagumo, Hodgkin-Huxley, Initial value problem, It{\^o} calculus, Stochastic differential equation, Stochastic PDEs",

author = "Hasan Alzubaidi and Hagen Gilsing and Tony Shardlow",

year = "2010",

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AU - Alzubaidi, Hasan

AU - Gilsing, Hagen

AU - Shardlow, Tony

PY - 2010/2/1

Y1 - 2010/2/1

N2 - 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.

AB - 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.

KW - FitzHugh-Nagumo

KW - Hodgkin-Huxley

KW - Initial value problem

KW - Itô calculus

KW - Stochastic differential equation

KW - Stochastic PDEs

UR - https://www.scopus.com/pages/publications/84920751835

U2 - 10.1093/acprof:oso/9780199235070.003.0012

DO - 10.1093/acprof:oso/9780199235070.003.0012

M3 - Book chapter

AN - SCOPUS:84920751835

SN - 9780199235070

BT - Stochastic Methods in Neuroscience

PB - Oxford University Press

ER -

Numerical Simulations of SDEs and SPDEs From Neural Systems Using SDELab

Abstract

Keywords

ASJC Scopus subject areas

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