Citation: | ZHANG Ying, DU Lin, YUE Xiao-le, HU Jian, FANG Tong. Stochastic Nonlinear Dynamics Analysis of Double-Well Duffing Systems Under Random Parametric Excitations[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1198-1207. doi: 10.21656/1000-0887.370257 |
[1] |
Holmes P. A nonlinear oscillator with a strange attractor[J]. Philosophical Transactions of the Royal Society A: Mathematical and Physical Sciences,1979,292(1394): 419-448.
|
[2] |
Nbendjo B R N, Tchoukuegno R, Woafo P. Active control with delay of vibration and chaos in a double-well Duffing oscillator[J]. Chaos, Solitons & Fractals,2003,18(2): 345-353.
|
[3] |
Marinca V, Herianu N. Explicit and exact solutions to cubic Duffing and double-well Duffing equations[J]. Mathematical and Computer Modelling,2011,53(5/6): 604-609.
|
[4] |
Beléndez A, Bernabeu G, Francés J, Méndeza D I, Marinia S. An accurate closed-form approximate solution for the quintic Duffing oscillator equation[J]. Mathematical and Computer Modelling,2010,52(3/4): 637-641.
|
[5] |
Syta A, Litak G, Lenci S, Scheffler M. Chaotic vibrations of the Duffing system with fractional damping[J]. Chaos,2014,24: 013107.
|
[6] |
Marinca V, Heri anu N. Periodic solutions of Duffing equation with strong non-linearity[J]. Chaos Solitons & Fractals,2008,37(1): 144-149.
|
[7] |
Cveticanin L. The approximate solving methods for the cubic Duffing equation based on the Jacobi elliptic functions[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2009,10(11/12): 1491-1516.
|
[8] |
Rong H, Xu W, Fang T. Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation[J]. Journal of Sound and Vibration,1998,210(4): 483-515.
|
[9] |
金肖玲, 黄志龙, 梁以德. 调制白噪声激励下的单自由度强非线性系统的近似瞬态响应概率密度[J]. 应用数学和力学, 2011,32(11): 1294-1305.(JIN Xiao-ling, HUANG Zhi-long, LEUNG Andrew Y T. Nonstationary probability densities of system response of strongly nonlinear single-degree-of-freedom system subject to modulated white noise excitation[J]. Applied Mathematics and Mechanics,2011,32(11): 1294-1305.(in Chinese))
|
[10] |
马少娟, 徐伟, 李伟. 基于Laguerre多项式逼近法的随机双势阱Duffing系统的分岔和混沌研究[J]. 物理学报, 2006,55(8): 4013-4019.(MA Shao-juan, XU Wei, LI Wei. Analysis of bifurcation and chaos in double-well Duffing system via Laguerre polynomial approximation[J]. Acta Physica Sinica,2006,55(8): 4013-4019.(in Chinese))
|
[11] |
武娟, 许勇. 加性二值噪声激励下Duffing系统的随机分岔[J]. 应用数学和力学, 2015,36(6): 593-599.(WU Juan, XU Yong. Stochastic bifurcations in a Duffing system driven by additive dichotomous noises[J]. Applied Mathematics and Mechanics,2015,36(6): 593-599.(in Chinese))
|
[12] |
GUO Yu, Luo A C J. Periodic motions in a double-well Duffing oscillator under periodic excitation through discrete implicit mappings[J]. International Journal of Dynamics and Control,2015. doi: 10.1007/s40435-015-0161-6.
|
[13] |
LIU Wen-yan, ZHU Wei-qiu, HUANG Zhi-long. Effect of bounded noise on chaotic motion of Duffing oscillator under parametric excitation[J]. Chaos Solitons & Fractals,2001,12(3): 527-537.
|
[14] |
XU Yong, LI Yong-ge, LIU Di, JIA Wan-tao, HUANG Hui. Responses of Duffing oscillator with fractional damping and random phase[J]. Nonlinear Dynamics,2013,74(3): 745-753.
|
[15] |
Spanos P D, Ghanem R. Stochastic finite element expansion for random media[J]. Journal of Engineering Mechanics,1989,115(5): 1035-1053.
|
[16] |
FANG Tong, LENG Xiao-lei, MA Xiao-ping, MENG Guang. λ-PDF and Gegenbauer polynomial approximation for dynamic response problems of random structures[J]. Acta Mechanica Sinica,2004,20(3): 292-298.
|
[17] |
ZHANG Ying, DU Lin, YUE Xiao-le, HAN Qun, FANG Tong. Analysis of symmetry breaking bifurcation in Duffing system with random parameter[J]. Computer Modeling in Engineering and Sciences,2015,106(1): 37-51.
|
[18] |
ZHANG Ying, DU Lin, YUE Xiao-le, HAN Qun, FANG Tong. Analysis of symmetry breaking bifurcation in Duffing system with random parameter[J]. Computer Modeling in Engineering and Sciences,2015,106(1): 37-51.
|
[19] |
ZHANG Ying, Rossetto B, XU Wei, YUE Xiao-le,FANG tong. Roles of chaotic saddle and basin of attraction in bifurcation and crisis analysis[J]. International Journal of Bifurcation and Chaos,2011,21(3): 903-915.
|
[20] |
刘式适, 刘式达. 特殊函数[M]. 北京: 气象出版社, 1988.(LIU Shi-kuo, LIU Shi-da. Special Function [M]. Beijing: China Meteorological Press, 1988.(in Chinese))
|