Noise-induced changes to the behaviour of semi-implicit Euler methods for stochastic delay differential equations undergoing bifurcation
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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. 462-470Publisher
ElsevierAdditional Links
http://www.sciencedirect.com/science/journal/03770427Type
ArticleLanguage
enDescription
This article is not available through ChesterRep.ISSN
0377-0427ae974a485f413a2113503eed53cd6c53
10.1016/j.cam.2008.04.017