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The mass of Brownian particle is fluctuant in a viscous medium, because the molecules of surrounding medium may randomly stick on it. This mass fluctuation influence on the system resonant behavior is studied by modeling it as a symmetric dichotomous noise. Using Shapiro-Loginov formula and Laplace transformation, the analytical expression of system steady response amplitude is presented. The corresponding numerical results are used to discuss system resonant behavior. Furthermore, the reliability of theoretical results is tested by simulation experiments. All the research results show that: 1) the system steady response is a simple harmonic vibration which has the same frequency as the driving signal; 2) with the variations of driving frequency, oscillator mass and noise parameters, the system presents real resonance, parameter induced resonance and stochastic resonance phenomenon, respectively; 3) because of the mass fluctuation, some new resonant forms are observed, such as one-peak and one-valley resonance, two-peak resonance, etc.
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Keywords:
- mass fluctuation noise /
- stochastic resonance /
- two-peak resonance
[1] Landau L D, Lifshitz E M (Translated by Li J F) 2007 Mechanics (5st Ed.) (Beijing: Higher Education Press) pp75-102 (in Chinese) [朗道L. D., 栗弗席兹E. M. 著, 李俊峰译 2007 力学(第五版)(北京: 高等教育出版社) 第75–102页]
[2] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Press) pp5, 32 (in Chinese) [胡岗 1994 随机力与非线性系统(上海: 上海科技教育出版社) 第5, 32页]
[3] Bao J D 2009 Random Simulation Method of Classical and Quantum Dissipation System (Beijing: Science Press) pp79-80 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (北京: 科学出版社) 第79-80页]
[4] Gitterman M 2004 Phys. Rev. E 69 041101
[5] Méndez V, Horsthemke W, Mestres G, Campos D 2011 Phys. Rev. E 84 041137
[6] Guo L M, Xu W, Ruan C L, Zhao Y 2008 Acta Phys. Sin. 57 7482 (in Chinese) [郭立敏, 徐伟, 阮春雷, 赵燕 2008 57 7482]
[7] Jin Y F, Hu H Y 2009 Acta Phys. Sin. 58 2895 (in Chinese) [靳艳飞, 胡海岩 2009 58 2895]
[8] Blum J, Wurm G, Kempf S, Poppe T 2000 Phys. Rev. Lett. 85 2426
[9] Pérez A T, Saville D, Soria C 2001 Europhys. Lett. 55 425
[10] Goldhirsch I, Zanetti G 1993 Phys. Rev. Lett. 70 1619
[11] Gitterman M, Klyatskin V I 2010 Phys. Rev. E 81 051139
[12] Gitterman M 2012 Physica A 391 3033
[13] Gitterman M 2012 Physica A 391 5343
[14] Portman J, Khasin M, Shaw S W, Dykman M I 2010 APS March Meeting Portland, USA, March 15-19, 2010 Abstract V14.010
[15] Luczka J, Hanggi P, Gadomski A 1995 Phys. Rev. E 51 5762
[16] Rubí J M, Gadomski A 2003 Physica A 326 333
[17] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[18] Gitterman M, Shapiro I 2011 J. Stat. Phys. 144 139
[19] Shapiro V E, Loginov V M 1978 Physica A 91 563
[20] Li P, Nie L R, Huang Q R, Sun X X 2011 Chin. Phys. B 21 050503
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[1] Landau L D, Lifshitz E M (Translated by Li J F) 2007 Mechanics (5st Ed.) (Beijing: Higher Education Press) pp75-102 (in Chinese) [朗道L. D., 栗弗席兹E. M. 著, 李俊峰译 2007 力学(第五版)(北京: 高等教育出版社) 第75–102页]
[2] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Press) pp5, 32 (in Chinese) [胡岗 1994 随机力与非线性系统(上海: 上海科技教育出版社) 第5, 32页]
[3] Bao J D 2009 Random Simulation Method of Classical and Quantum Dissipation System (Beijing: Science Press) pp79-80 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (北京: 科学出版社) 第79-80页]
[4] Gitterman M 2004 Phys. Rev. E 69 041101
[5] Méndez V, Horsthemke W, Mestres G, Campos D 2011 Phys. Rev. E 84 041137
[6] Guo L M, Xu W, Ruan C L, Zhao Y 2008 Acta Phys. Sin. 57 7482 (in Chinese) [郭立敏, 徐伟, 阮春雷, 赵燕 2008 57 7482]
[7] Jin Y F, Hu H Y 2009 Acta Phys. Sin. 58 2895 (in Chinese) [靳艳飞, 胡海岩 2009 58 2895]
[8] Blum J, Wurm G, Kempf S, Poppe T 2000 Phys. Rev. Lett. 85 2426
[9] Pérez A T, Saville D, Soria C 2001 Europhys. Lett. 55 425
[10] Goldhirsch I, Zanetti G 1993 Phys. Rev. Lett. 70 1619
[11] Gitterman M, Klyatskin V I 2010 Phys. Rev. E 81 051139
[12] Gitterman M 2012 Physica A 391 3033
[13] Gitterman M 2012 Physica A 391 5343
[14] Portman J, Khasin M, Shaw S W, Dykman M I 2010 APS March Meeting Portland, USA, March 15-19, 2010 Abstract V14.010
[15] Luczka J, Hanggi P, Gadomski A 1995 Phys. Rev. E 51 5762
[16] Rubí J M, Gadomski A 2003 Physica A 326 333
[17] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[18] Gitterman M, Shapiro I 2011 J. Stat. Phys. 144 139
[19] Shapiro V E, Loginov V M 1978 Physica A 91 563
[20] Li P, Nie L R, Huang Q R, Sun X X 2011 Chin. Phys. B 21 050503
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