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研究了有界噪声与谐和激励作用下的Duffing-Rayleigh振子的动力学行为.首先运用随机Melnikov过程方法得到系统出现混沌的条件,结果表明随着非线性阻尼参数的增加系统会从混沌运动到周期运动,随着Wiener过程强度参数的增加,系统由混沌进入周期的临界幅值会先递增后不变.最后,用两类数值方法即最大Lyapunov指数与Poincare截面验证了上述结果.
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关键词:
- 有界噪声 /
- 随机Melnikov过程 /
- 混沌运动 /
- 周期运动
In this paper,the dynamic behavior of Duffing-Rayleigh oscillator subjected to combined bounded noise and harmonic excitations is investigated. Theoretically, the random Melnikov's method is used to establish the conditions of existence of chaotic motion. The result implies that the chaotic motion of the system turns into the periodic motion with the increase of nonlinear damping parameter, and the threshold of random excitation amplitude for the system to change from chaotic to periodic motion in the oscillator turns from increasing to constant as the intensity of the noise increases. Numerically,the largest Lyapunov exponents and the Poincare maps are also used for verifying the conclusion.-
Keywords:
- bounded noise /
- random Melnikov process /
- chaotic motion /
- periodic motion
[1] Venkatesan A, Lakshmanan M 1997 Phys. Rev. E 56 6321
[2] Kao Y H 1993 Phys. Rev. E 2514
[3] Bulsara A R, Schieve W C, Jacobs E W 1990 Phys. Rev. A 41 668
[4] Xie W C 1994 Nonlinear and Stochastic Dynamics. 78 215
[5] Wei J G, Leng G 1997 Applied Mathematics and Computation 88 77
[6] Kenfack A, Kofane T C 1998 Physica Scripta 56 659
[7] Yang X L,Xu W,Sun Z K 2006 Acta Phys.Sin. 55 1678(in Chinese)[杨晓丽、徐 伟、孙中奎 2006 物理学报 55 1678]
[8] Lei Y M, Xu W 2007 Acta Phys. Sin. 56 5103(in Chinese)[雷佑铭、徐 伟 2007 物理学报 56 5103]
[9] Yang X L, Xu W 2009 Acta Phys Sin. 58 3722(in Chinese)[杨晓丽、徐 伟 2009 物理学报 58 3722]
[10] Siewe Siewe M, Tchawoua C, Woafo P 2010 Mechanics Research Communications 37 363
[11] Siewe Siewe M, Cao H J, Sanjuan M A F 2009 Chaos, Solitons and Fractals 39 1092
[12] Xie W X, Xu W, Cai L 2006 Applied Mathematics and Computation 172 1212
[13] Frey M, Simiu E 1993 Physica D 63 321
[14] Liu W Y, Zhu W Q, Huang Z L 2001 Chaos , Solitons and Fractals 88 527
[15] Lin Y K, Cai G Q 1995 Probabilistic structural dynamics : advanced theory and applications (New York : Mc Graw Hill)
[16] Liu Z R 2002 The analytical method of chaos (Shanghai: Shanghai University Press )p56(in Chinese) [刘增荣 2002 混沌研究中的解析方法 (上海:上海大学出版社) 第56页]
[17] Han Q, Zhang S Y, Yang G T 1999 Applied Mathematics and Mechanics8 776(in Chinese) [韩 强、张善元、杨桂通 1999 应用数学和力学 8 776]
[18] Li Y J 2002 M.S. Dissertation (Changchun: Jilin University) (in Chinese)[李亚峻 2002 硕士学位论文(长春:吉林大学)]
[19] Wolf A, Swift J, Swinnery H, Vastano A 1985 Physica D 16 285
-
[1] Venkatesan A, Lakshmanan M 1997 Phys. Rev. E 56 6321
[2] Kao Y H 1993 Phys. Rev. E 2514
[3] Bulsara A R, Schieve W C, Jacobs E W 1990 Phys. Rev. A 41 668
[4] Xie W C 1994 Nonlinear and Stochastic Dynamics. 78 215
[5] Wei J G, Leng G 1997 Applied Mathematics and Computation 88 77
[6] Kenfack A, Kofane T C 1998 Physica Scripta 56 659
[7] Yang X L,Xu W,Sun Z K 2006 Acta Phys.Sin. 55 1678(in Chinese)[杨晓丽、徐 伟、孙中奎 2006 物理学报 55 1678]
[8] Lei Y M, Xu W 2007 Acta Phys. Sin. 56 5103(in Chinese)[雷佑铭、徐 伟 2007 物理学报 56 5103]
[9] Yang X L, Xu W 2009 Acta Phys Sin. 58 3722(in Chinese)[杨晓丽、徐 伟 2009 物理学报 58 3722]
[10] Siewe Siewe M, Tchawoua C, Woafo P 2010 Mechanics Research Communications 37 363
[11] Siewe Siewe M, Cao H J, Sanjuan M A F 2009 Chaos, Solitons and Fractals 39 1092
[12] Xie W X, Xu W, Cai L 2006 Applied Mathematics and Computation 172 1212
[13] Frey M, Simiu E 1993 Physica D 63 321
[14] Liu W Y, Zhu W Q, Huang Z L 2001 Chaos , Solitons and Fractals 88 527
[15] Lin Y K, Cai G Q 1995 Probabilistic structural dynamics : advanced theory and applications (New York : Mc Graw Hill)
[16] Liu Z R 2002 The analytical method of chaos (Shanghai: Shanghai University Press )p56(in Chinese) [刘增荣 2002 混沌研究中的解析方法 (上海:上海大学出版社) 第56页]
[17] Han Q, Zhang S Y, Yang G T 1999 Applied Mathematics and Mechanics8 776(in Chinese) [韩 强、张善元、杨桂通 1999 应用数学和力学 8 776]
[18] Li Y J 2002 M.S. Dissertation (Changchun: Jilin University) (in Chinese)[李亚峻 2002 硕士学位论文(长春:吉林大学)]
[19] Wolf A, Swift J, Swinnery H, Vastano A 1985 Physica D 16 285
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