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dc.contributor.advisorNaess, Arvidnb_NO
dc.contributor.authorMo, Eiriknb_NO
dc.date.accessioned2014-12-19T13:29:30Z
dc.date.available2014-12-19T13:29:30Z
dc.date.created2008-01-02nb_NO
dc.date.issued2008nb_NO
dc.identifier123119nb_NO
dc.identifier.isbn978-82-471-6213-2nb_NO
dc.identifier.urihttp://hdl.handle.net/11250/249727
dc.description.abstractThe numerical path integration method for solving stochastic differential equations is extended to solve systems up to six spatial dimensions, angular variables, and highly nonlinear systems - including systems that results in discontinuities in the response probability density function of the system. Novel methods to stabilize the numerical method and increase computation speed are presented and discussed. This includes the use of the fast Fourier transform (FFT) and some new spline interpolation methods. Some sufficient criteria for the path integration theory to be applicable is also presented. The development of complex numerical code is made possible through automatic code generation by scripting. The resulting code is applied to chaotic dynamical systems by adding a Gaussian noise term to the deterministic equation. Various methods and approximations to compute the largest Lyapunov exponent of these systems are presented and illustrated, and the results are compared. Finally, it is shown that the location and size of the additive noise term affects the results, and it is shown that additive noise for specific systems could make a non-chaotic system chaotic, and a chaotic system non-chaotic.nb_NO
dc.languageengnb_NO
dc.publisherFakultet for informasjonsteknologi, matematikk og elektroteknikknb_NO
dc.relation.ispartofseriesDoktoravhandlinger ved NTNU, 1503-8181; 2008:18nb_NO
dc.subjectspline interpolationen_GB
dc.subjectprobability density functionen_GB
dc.subjectlyapunov exponenten_GB
dc.subjectnonlinear dynamicsen_GB
dc.subjectSOCIAL SCIENCES: Statistics, computer and systems science: Statisticsen_GB
dc.titleNonlinear stochastic dynamics and chaos by numerical path integrationnb_NO
dc.typeDoctoral thesisnb_NO
dc.source.pagenumber239nb_NO
dc.contributor.departmentNorges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikknb_NO
dc.description.degreePhD i matematikknb_NO
dc.description.degreePhD in Mathematicsen_GB


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