An algorithm for Melnikov functions and application to a chaotic rotor

Xu, J. X., Yan, R. and Zhang, W. N. (2005) An algorithm for Melnikov functions and application to a chaotic rotor. Siam Journal On Scientific Computing, 26 5: 1525-1546. doi:10.1137/S1064827503420726

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Author Xu, J. X.
Yan, R.
Zhang, W. N.
Title An algorithm for Melnikov functions and application to a chaotic rotor
Journal name Siam Journal On Scientific Computing   Check publisher's open access policy
ISSN 1064-8275
Publication date 2005
Sub-type Article (original research)
DOI 10.1137/S1064827503420726
Open Access Status File (Publisher version)
Volume 26
Issue 5
Start page 1525
End page 1546
Total pages 22
Place of publication Philadelphia, PA, United States
Publisher Society for Industrial and Applied Mathematics
Language eng
Abstract In 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.
Keyword Mathematics, Applied
mathematical modeling
Melnikov function
modulus of continuity
oscillatory integrand
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Information Technology and Electrical Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 7 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 6 times in Scopus Article | Citations
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Created: Fri, 25 Jan 2008, 16:34:32 EST