Predicting changes in dynamical behaviour in solutions to stochastic delay differential equations

Hdl Handle:
http://hdl.handle.net/10034/72778
Title:
Predicting changes in dynamical behaviour in solutions to stochastic delay differential equations
Authors:
Norton, Stewart J.; Ford, Neville J.
Abstract:
This article considers numerical approximations to parameter-dependent linear and logistic stochastic delay differential equations with multiplicative noise. The aim of the investigation is to explore the parameter values at which there are changes in qualitative behaviour of the solutions. One may use a phenomenological approach but a more analytical approach would be attractive. A possible tool in this analysis is the calculation of the approximate local Lyapunov exponents. In this paper we show that the phenomenological approach can be used effectively to estimate bifurcation parameters for deterministic linear equations but one needs to use the dynamical approach for stochastic equations.
Affiliation:
University of Chester
Citation:
Communications on Pure and Applied Mathematics, 2006, 5(2), pp. 367-382
Publisher:
AIMS Press
Journal:
Communications on Pure and Applied Mathematics
Publication Date:
Jun-2006
URI:
http://hdl.handle.net/10034/72778
Additional Links:
http://aimsciences.org
Type:
Article
Language:
en
Description:
This article is not available through ChesterRep.
ISSN:
1534-0392
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorNorton, Stewart J.en
dc.contributor.authorFord, Neville J.en
dc.date.accessioned2009-07-07T14:21:57Zen
dc.date.available2009-07-07T14:21:57Zen
dc.date.issued2006-06en
dc.identifier.citationCommunications on Pure and Applied Mathematics, 2006, 5(2), pp. 367-382en
dc.identifier.issn1534-0392en
dc.identifier.urihttp://hdl.handle.net/10034/72778en
dc.descriptionThis article is not available through ChesterRep.en
dc.description.abstractThis article considers numerical approximations to parameter-dependent linear and logistic stochastic delay differential equations with multiplicative noise. The aim of the investigation is to explore the parameter values at which there are changes in qualitative behaviour of the solutions. One may use a phenomenological approach but a more analytical approach would be attractive. A possible tool in this analysis is the calculation of the approximate local Lyapunov exponents. In this paper we show that the phenomenological approach can be used effectively to estimate bifurcation parameters for deterministic linear equations but one needs to use the dynamical approach for stochastic equations.en
dc.language.isoenen
dc.publisherAIMS Pressen
dc.relation.urlhttp://aimsciences.orgen
dc.subjectstochastic delay differential equationsen
dc.subjectbifurcationsen
dc.subjectLyapunov exponentsen
dc.titlePredicting changes in dynamical behaviour in solutions to stochastic delay differential equationsen
dc.typeArticleen
dc.contributor.departmentUniversity of Chesteren
dc.identifier.journalCommunications on Pure and Applied Mathematicsen
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