Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation. (20th September 2016)

• Record Type: Journal Article
• Authors: Zhang, Ying; Yue, Xiaole; Du, Lin; Wang, Liang; Fang, Tong
• Other Names: Thai Tai Academic Editor.
• Is Part Of: Shock and vibration. Volume 2016(2016)
• Publication Date: 2016-09-20
• Subjects: Shock (Mechanics) -- Periodicals; Vibration -- Periodicals; 534.5
• DOI: 10.1155/2016/6109062
• Languages: English
• ISSNs: 1070-9622

Abstract

Abstract : The generation and evolution of chaotic motion in double-well Duffing oscillator under harmonic parametrical excitation are investigated. Firstly, the complex dynamical behaviors are studied by applying multibifurcation diagram and Poincaré sections. Secondly, by means of Melnikov's approach, the threshold value of parameterμ for generation of chaotic behavior in Smale horseshoe sense is calculated. By the numerical simulation, it is obvious that asμ exceeds this threshold value, the behavior of Duffing oscillator is still steady-state periodic but the transient motion is chaotic; until the top Lyapunov exponent turns to positive, the motion of system turns to permanent chaos. Therefore, in order to gain an insight into the evolution of chaotic behavior afterμ passing the threshold value, the transient motion, basin of attraction, and basin boundary are also investigated.