An algorithm for Melnikov functions and application to a chaotic rotor

Xu, JX, Yan, R and Zhang, WN (2005) An algorithm for Melnikov functions and application to a chaotic rotor. Siam Journal On Scientific Computing, 26 5: 1525-1546.


Author Xu, JX
Yan, R
Zhang, WN
Title An algorithm for Melnikov functions and application to a chaotic rotor
Journal name Siam Journal On Scientific Computing  (ERA 2012 Listed)    (ERA 2010 Rank A)   Check publisher's open access policy
Publication date 2005
Sub-type Article
DOI 10.1137/S1064827503420726
Volume number 26
Issue number 5
ISSN 1064-8275
Start page 1525
End page 1546
Total pages 22
Place of publication Philadelphia
Publisher Siam Publications
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
chaos
modulus of continuity
oscillatory integrand
Gyrostat
Orbits
Perturbations
Bifurcations
Computation
Integrals
Motion
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article
Collection: School of Information Technology and Electrical Engineering Publications
 
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