Noise-induced changes to the bifurcation behaviour of semi-implicit Euler methods for stochastic delay differential equations

Hdl Handle:
http://hdl.handle.net/10034/346642
Title:
Noise-induced changes to the bifurcation behaviour of semi-implicit Euler methods for stochastic delay differential equations
Authors:
Ford, Neville J.; Norton, Stewart J.
Abstract:
We are concerned with estimating parameter values at which bifurcations occur in stochastic delay differential equations. After a brief review of bifurcation, we employ a numerical approach and consider how bifurcation values are influenced by the choice of numerical scheme and the step length and by the level of white noise present in the equation. In this paper we provide a formulaic relationship between the estimated bifurcation value, the level of noise, the choice of numerical scheme and the step length. We are able to show that in the presence of noise there maybe some loss of order in the accuracy of the approximation to the true bifurcation value compared to the use of the same approach in the absence of noise.
Affiliation:
University of Chester
Citation:
Chester : University of Chester, 2007
Publisher:
University of Chester
Publication Date:
2007
URI:
http://hdl.handle.net/10034/346642
Additional Links:
http://www.chester.ac.uk
Type:
Technical Report
Language:
en
Series/Report no.:
Applied Mathematics Group Research Report; 2007 : 5
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorFord, Neville J.en
dc.contributor.authorNorton, Stewart J.en
dc.date.accessioned2015-03-13T15:06:58Zen
dc.date.available2015-03-13T15:06:58Zen
dc.date.issued2007en
dc.identifier.citationChester : University of Chester, 2007en
dc.identifier.urihttp://hdl.handle.net/10034/346642en
dc.description.abstractWe are concerned with estimating parameter values at which bifurcations occur in stochastic delay differential equations. After a brief review of bifurcation, we employ a numerical approach and consider how bifurcation values are influenced by the choice of numerical scheme and the step length and by the level of white noise present in the equation. In this paper we provide a formulaic relationship between the estimated bifurcation value, the level of noise, the choice of numerical scheme and the step length. We are able to show that in the presence of noise there maybe some loss of order in the accuracy of the approximation to the true bifurcation value compared to the use of the same approach in the absence of noise.en
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.relation.ispartofseriesApplied Mathematics Group Research Reporten
dc.relation.ispartofseries2007 : 5en
dc.relation.urlhttp://www.chester.ac.uken
dc.subjectstochastic delay equationsen
dc.subjectbifurcationsen
dc.subjectnumerical methodsen
dc.titleNoise-induced changes to the bifurcation behaviour of semi-implicit Euler methods for stochastic delay differential equationsen
dc.typeTechnical Reporten
dc.contributor.departmentUniversity of Chesteren
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