Chaotic Behavior of the Biharmonic Dynamics System
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-03-26
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
Motion of a biharmonic system under action of small periodic force and small damped force is studied.
The biharmonic oscillator is a physical system acting under a biharmonic force like asinθ+bsin2θ.
The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes.
The biharmonic oscillator performs chaotic motion near separatrixes under small perturbations.
Melnikov method gives analytical criterion for heteroclinic chaos in terms of system parameters.
A transition from chaotic to regular motion of the biharmonic oscillator was found as the heteroclinic chaos can be removed by increasing the coefficient of a damping force.
The analytical results obtained using Melnikov method have been confirmed by a good match with numeric research.
American Psychological Association (APA)
Aslanov, Vladimir S.. 2009. Chaotic Behavior of the Biharmonic Dynamics System. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-18.
https://search.emarefa.net/detail/BIM-463154
Modern Language Association (MLA)
Aslanov, Vladimir S.. Chaotic Behavior of the Biharmonic Dynamics System. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-18.
https://search.emarefa.net/detail/BIM-463154
American Medical Association (AMA)
Aslanov, Vladimir S.. Chaotic Behavior of the Biharmonic Dynamics System. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-18.
https://search.emarefa.net/detail/BIM-463154
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-463154
