Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator

Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator

Chaos analysis and control of relative rotation nonlinear dynamic system with Mathieu-Duffing oscillator are investigated. By using Lagrange equation, the dynamics equation of relative rotation system has been established. Melnikov’s method is applied to predict the chaotic behavior of this system....

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Main Authors: Yu Zhang, Longsuo Li
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/348462
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spelling doaj-a60c6af8bbaa4d5d996d65871d2465c92020-11-25T00:34:20ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/348462348462Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing OscillatorYu Zhang0Longsuo Li1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaChaos analysis and control of relative rotation nonlinear dynamic system with Mathieu-Duffing oscillator are investigated. By using Lagrange equation, the dynamics equation of relative rotation system has been established. Melnikov’s method is applied to predict the chaotic behavior of this system. Moreover, the chaotic dynamical behavior can be controlled by adding the Gaussian white noise to the proposed system for the sake of changing chaos state into stable state. Through numerical calculation, the Poincaré map analysis and phase portraits are carried out to confirm main results.http://dx.doi.org/10.1155/2015/348462
collection DOAJ
language English
format Article
sources DOAJ
author Yu Zhang
Longsuo Li
spellingShingle Yu Zhang
Longsuo Li
Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator
Mathematical Problems in Engineering
author_facet Yu Zhang
Longsuo Li
author_sort Yu Zhang
title Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator
title_short Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator
title_full Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator
title_fullStr Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator
title_full_unstemmed Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator
title_sort chaos analysis and control of relative rotation system with mathieu-duffing oscillator
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description Chaos analysis and control of relative rotation nonlinear dynamic system with Mathieu-Duffing oscillator are investigated. By using Lagrange equation, the dynamics equation of relative rotation system has been established. Melnikov’s method is applied to predict the chaotic behavior of this system. Moreover, the chaotic dynamical behavior can be controlled by adding the Gaussian white noise to the proposed system for the sake of changing chaos state into stable state. Through numerical calculation, the Poincaré map analysis and phase portraits are carried out to confirm main results.
url http://dx.doi.org/10.1155/2015/348462
work_keys_str_mv AT yuzhang chaosanalysisandcontrolofrelativerotationsystemwithmathieuduffingoscillator
AT longsuoli chaosanalysisandcontrolofrelativerotationsystemwithmathieuduffingoscillator
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