Title of article :
Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation
Author/Authors :
Zhang, Ying Department of Applied Mathematics - Northwestern Polytechnical University, China , Yue,Xiaole Department of Applied Mathematics - Northwestern Polytechnical University, China , Du,Lin Department of Applied Mathematics - Northwestern Polytechnical University, China , Wang, Liang Department of Applied Mathematics - Northwestern Polytechnical University, China , Fang, Tong Department of Engineering Mechanics - Northwestern Polytechnical University, China
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 parameter for generation of chaotic behavior in Smale horseshoe sense is calculated. By the numerical simulation, it is obvious that as 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 after passing the threshold value, the transient motion, basin of attraction, and basin boundary are also investigated.
Keywords :
Generation and Evolution , Chaos , Double-Well , Parametrical Excitation , Duffing Oscillator under
Journal title :
Shock and Vibration
