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Noise-induced changes to the behaviour of semi-implicit Euler methods for stochastic delay differential equations undergoing bifurcation
Ford, Neville J. Norton, Stewart J.
Ford, Neville J.
Norton, Stewart J.
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Publication Date
2009-07-15
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Abstract
This article discusses 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 may be 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.
Citation
Journal of Computational and Applied Mathematics, 2009, 229(2), pp. 462-470
Publisher
Elsevier
Journal
Journal of Computational and Applied Mathematics
Research Unit
DOI
10.1016/j.cam.2008.04.017
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Article
Language
en
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ISSN
0377-0427