In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The fourth-order Runge–Kutta method and tenth-order CFE-Euler method are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on system dynamics is investigated using phase diagram, bifurcation diagram and Poincaré map. The bifurcation diagram is introduced to exam the effect of excitation amplitude, frequency, and damping coefficient on the Duffing system with fractional order damping. The analysis results show that the fractional order damped Duffing system exhibits periodic motion, chaos, periodic motion, chaos, and periodic motion in turn when the fractional order varies from 0.1 to 2.0. The period doubling bifurcation route to chaos and inverse period doubling bifurcation out of chaos are clearly observed in the bifurcation diagrams with various excitation amplitude, frequency, and damping coefficient.
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e-mail: caojy@mail.xjtu.edu.cn
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October 2010
Research Papers
Nonlinear Dynamics of Duffing System With Fractional Order Damping
Junyi Cao,
Junyi Cao
State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics,
e-mail: caojy@mail.xjtu.edu.cn
Xi’an Jiaotong University
, Xi’an 710049, China
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Chengbin Ma,
Chengbin Ma
University of Michigan–Shanghai Jiaotong University Joint Institute,
Shanghai Jiaotong University
, Shanghai 200240, China
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Hang Xie,
Hang Xie
State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics,
Xi’an Jiaotong University
, Xi’an 710049, China
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Zhuangde Jiang
Zhuangde Jiang
State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics,
Xi’an Jiaotong University
, Xi’an 710049, China
Search for other works by this author on:
Junyi Cao
State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics,
Xi’an Jiaotong University
, Xi’an 710049, Chinae-mail: caojy@mail.xjtu.edu.cn
Chengbin Ma
University of Michigan–Shanghai Jiaotong University Joint Institute,
Shanghai Jiaotong University
, Shanghai 200240, China
Hang Xie
State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics,
Xi’an Jiaotong University
, Xi’an 710049, China
Zhuangde Jiang
State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics,
Xi’an Jiaotong University
, Xi’an 710049, ChinaJ. Comput. Nonlinear Dynam. Oct 2010, 5(4): 041012 (6 pages)
Published Online: August 12, 2010
Article history
Received:
June 12, 2009
Revised:
October 19, 2009
Online:
August 12, 2010
Published:
August 12, 2010
Citation
Cao, J., Ma, C., Xie, H., and Jiang, Z. (August 12, 2010). "Nonlinear Dynamics of Duffing System With Fractional Order Damping." ASME. J. Comput. Nonlinear Dynam. October 2010; 5(4): 041012. https://doi.org/10.1115/1.4002092
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