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Noise-induced changes to the bifurcation behaviour of semi-implicit Euler methods for stochastic delay differential equations
Ford, Neville J. Norton, Stewart J.
Ford, Neville J.
Norton, Stewart J.
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2007
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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.
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Chester : University of Chester, 2007
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University of Chester
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Report
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en
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Applied Mathematics Group Research Report
2007 : 5
2007 : 5