International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 319179, 18 pages
Research Article

Chaotic Behavior of the Biharmonic Dynamics System

Theoretical Mechanics Department, Faculty of Aircraft Construction, Samara State Aerospace University (SSAU), 34 Moscovskoe shosse, 443086 Samara, Russia

Received 31 July 2008; Accepted 13 January 2009

Academic Editor: Peter Basarab-Horwath

Copyright © 2009 Vladimir S. Aslanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.