Predicting changes in dynamical behaviour in solutions to stochastic delay differential equations
| dc.contributor.author | Norton, Stewart J. | * |
| dc.contributor.author | Ford, Neville J. | * |
| dc.date.accessioned | 2009-07-07T14:21:57Z | |
| dc.date.available | 2009-07-07T14:21:57Z | |
| dc.date.issued | 2006-06 | |
| dc.identifier.citation | Communications on Pure and Applied Mathematics, 2006, 5(2), pp. 367-382 | en |
| dc.identifier.issn | 1534-0392 | en |
| dc.identifier.uri | http://hdl.handle.net/10034/72778 | |
| dc.description | This article is not available through ChesterRep. | en |
| dc.description.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. | |
| dc.language.iso | en | en |
| dc.publisher | AIMS Press | en |
| dc.relation.url | http://aimsciences.org | en |
| dc.subject | stochastic delay differential equations | en |
| dc.subject | bifurcations | en |
| dc.subject | Lyapunov exponents | en |
| dc.title | Predicting changes in dynamical behaviour in solutions to stochastic delay differential equations | en |
| dc.type | Article | en |
| dc.contributor.department | University of Chester | en |
| dc.identifier.journal | Communications on Pure and Applied Mathematics | |
| html.description.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. |