Using approximations to Lyapunov exponents to predict changes in dynamical behaviour in numerical solutions to stochastic delay differential equations

Hdl Handle:
http://hdl.handle.net/10034/72779
Title:
Using approximations to Lyapunov exponents to predict changes in dynamical behaviour in numerical solutions to stochastic delay differential equations
Authors:
Ford, Neville J.; Norton, Stewart J.
Abstract:
This book chapter explores the parameter values at which there are changes in qualitative behaviour of the numerical solutions to parameter-dependent linear stochastic delay differential equations with multiplicative noise. A possible tool in this analysis is the calculation of the approximate local Lyapunov exponents. We show that estimates for the maximal local Lyapunov exponent have predictable distributions dependent upon the parameter values and the fixed step length of the numerical method, and that changes in the qualitative behaviour of the solutions occur at parameter values that depend on the step length.
Affiliation:
University of Chester
Citation:
In A. Iske & J. Levesley (Eds.), Algorithms for Approximation, V (pp. 309-318). Berlin: Springer, 2007.
Publisher:
Springer
Publication Date:
2007
URI:
http://hdl.handle.net/10034/72779
DOI:
10.1007/978-3-540-46551-5_24
Additional Links:
http://www.springerlink.com
Type:
Book chapter
Language:
en
Description:
This book chapter is not available through ChesterRep.
ISSN:
9783540332831; 9783540465515
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorFord, Neville J.en
dc.contributor.authorNorton, Stewart J.en
dc.date.accessioned2009-07-07T14:23:33Zen
dc.date.available2009-07-07T14:23:33Zen
dc.date.issued2007en
dc.identifier.citationIn A. Iske & J. Levesley (Eds.), Algorithms for Approximation, V (pp. 309-318). Berlin: Springer, 2007.en
dc.identifier.issn9783540332831en
dc.identifier.issn9783540465515en
dc.identifier.doi10.1007/978-3-540-46551-5_24en
dc.identifier.urihttp://hdl.handle.net/10034/72779en
dc.descriptionThis book chapter is not available through ChesterRep.en
dc.description.abstractThis book chapter explores the parameter values at which there are changes in qualitative behaviour of the numerical solutions to parameter-dependent linear stochastic delay differential equations with multiplicative noise. A possible tool in this analysis is the calculation of the approximate local Lyapunov exponents. We show that estimates for the maximal local Lyapunov exponent have predictable distributions dependent upon the parameter values and the fixed step length of the numerical method, and that changes in the qualitative behaviour of the solutions occur at parameter values that depend on the step length.en
dc.language.isoenen
dc.publisherSpringeren
dc.relation.urlhttp://www.springerlink.comen
dc.subjectLyapunov exponentsen
dc.subjectstochastic delay differential equationsen
dc.titleUsing approximations to Lyapunov exponents to predict changes in dynamical behaviour in numerical solutions to stochastic delay differential equationsen
dc.typeBook chapteren
dc.contributor.departmentUniversity of Chesteren
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