Please use this identifier to cite or link to this item: https://doi.org/10.1137/S1064827503420726
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dc.titleAn algorithm for Melnikov functions and application to a chaotic rotor
dc.contributor.authorJian-Xin, X.
dc.contributor.authorYan, R.
dc.contributor.authorZhang, W.
dc.date.accessioned2014-06-17T02:37:51Z
dc.date.available2014-06-17T02:37:51Z
dc.date.issued2005
dc.identifier.citationJian-Xin, X., Yan, R., Zhang, W. (2005). An algorithm for Melnikov functions and application to a chaotic rotor. SIAM Journal on Scientific Computing 26 (5) : 1525-1546. ScholarBank@NUS Repository. https://doi.org/10.1137/S1064827503420726
dc.identifier.issn10648275
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/54987
dc.description.abstractIn this work we study a dynamical system with a complicated nonlinearity, which describes oscillation of a turbine rotor, and give an algorithm to compute Melnikov functions for analysis of its chaotic behavior. We first derive the rotor model whose nonlinear term brings difficulties to investigating the distribution and qualitative properties of its equilibria. This nonlinear model provides a typical example of a system for which the homoclinic and heteroclinic orbits cannot be analytically determined. In order to apply Melnikov's method to make clear the underlying conditions for chaotic motion, we present a generic algorithm that provides a systematic procedure to compute Melnikov functions numerically. Substantial analysis is done so that the numerical approximation precision at each phase of the computation can be guaranteed. Using the algorithm developed in this paper, it is straightforward to obtain a sufficient condition for chaotic motion under damping and periodic external excitation, whenever the rotor parameters are given. © 2005 Society for Industrial and Applied Mathematics.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1137/S1064827503420726
dc.sourceScopus
dc.subjectChaos
dc.subjectMathematical modeling
dc.subjectMelnikov function
dc.subjectModulus of continuity
dc.subjectOscillatory integrand
dc.typeArticle
dc.contributor.departmentELECTRICAL & COMPUTER ENGINEERING
dc.description.doi10.1137/S1064827503420726
dc.description.sourcetitleSIAM Journal on Scientific Computing
dc.description.volume26
dc.description.issue5
dc.description.page1525-1546
dc.description.codenSJOCE
dc.identifier.isiut000229475200004
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