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Shock and Vibration
Volume 2016 (2016), Article ID 9471423, 10 pages
Research Article

Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators

1Key Laboratory of Vibration Control and Structural Safety, Guangzhou University, Guangzhou 510405, China
2Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, China

Received 28 May 2015; Revised 23 August 2015; Accepted 26 August 2015

Academic Editor: Chia-Ming Chang

Copyright © 2016 Yang-Yang Chen et al. 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.


The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure. The homoclinic solution of the self-excited Helmholtz-Duffing oscillator can also be obtained by an extended hyperbolic perturbation method. The application of the present homoclinic solutions to the chaos prediction of the nonautonomous Helmholtz-Duffing oscillator is performed. Effectiveness and advantage of the present solutions are shown by comparisons.