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Mathematical Problems in Engineering
Volume 2017, Article ID 3769870, 8 pages
Research Article

Chaotic Motion in Forced Duffing System Subject to Linear and Nonlinear Damping

Department of Construction Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung, Taiwan

Correspondence should be addressed to Tai-Ping Chang; wt.ude.tsufkn.smcc@gnahcpt

Received 6 December 2016; Accepted 16 January 2017; Published 31 January 2017

Academic Editor: Jonathan N. Blakely

Copyright © 2017 Tai-Ping Chang. 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.


This paper investigates the chaotic motion in forced Duffing oscillator due to linear and nonlinear damping by using Melnikov technique. In particular, the critical value of the forcing amplitude of the nonlinear system is calculated by Melnikov technique. Further, the top Lyapunov exponent of the nonlinear system is evaluated by Wolf’s algorithm to determine whether the chaotic phenomenon of the nonlinear system actually occurs. It is concluded that the chaotic motion of the nonlinear system occurs when the forcing amplitude exceeds the critical value, and the linear and nonlinear damping can generate pronounced effects on the chaotic behavior of the forced Duffing oscillator.