In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The four order Runge-Kutta method and ten order CFE-Euler methods are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on the system dynamics is investigated using phase diagrams, bifurcation diagrams and Poincare map. The bifurcation diagram is also used to exam the effects of excitation amplitude and frequency on Duffing system with fractional order damping. The analysis results show that the fractional order damped Duffing system exhibits period motion, chaos, period motion, chaos, period motion in turn when the fractional order changes from 0.1 to 2.0. A period doubling route to chaos is clearly observed.
- Design Engineering Division and Computers in Engineering Division
Nonlinear Dynamics of Duffing System With Fractional Order Damping
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Cao, J, Ma, C, Xie, H, & Jiang, Z. "Nonlinear Dynamics of Duffing System With Fractional Order Damping." Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C. San Diego, California, USA. August 30–September 2, 2009. pp. 1003-1009. ASME. https://doi.org/10.1115/DETC2009-86401
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