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研究了高频信号和微弱低频信号同时激励下线性时滞反馈对过阻尼双稳系统和Duffing振子系统中振动共振现象的影响. 解析分析和数值结果都表明, 系统对低频信号的响应幅值增益随时滞参数的变化同时呈现两种不同的周期性关系, 其周期分别为输入的高频信号和低频信号的周期. 数值结果还表明, 对不存在经典振动共振现象的单稳Duffing系统, 通过调节时滞参数也可以引发振动共振现象. 使用时滞反馈不仅可以有效地控制振动共振, 还可以进一步增强系统对微弱低频信号的响应.
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关键词:
- 双稳系统 /
- Duffing 系统 /
- 线性时滞反馈 /
- 振动共振
Under the excitations of the high-frequency and weak low-frequency signals, the effects of linear time delay feedback on the vibrational resonance in overdamped bistable system and Duffing systems are investigated respectively. Both the analytical and the numerical results show that the response amplitude of the system to the low-frequency signal varies periodically with the delay parameter simultaneously (with two different periods, i.e., the periods of the two exciting signals). Numerical results also indicate that the delay feedback can induce vibrational resonance in the monostable Duffing system in which there exists no traditional vibrational resonance. By adjusting the delay parameter, not only the vibrational resonance can be effectively controlled, but also the response of the system to the weak low-frequency signal can be further improved.-
Keywords:
- bistable system /
- Duffing system /
- linear time delay feedback /
- vibrational resonance
[1] Knoblauch A, Palm G 2005 BioSystems 79 83
[2] Su D, Chiu M, Chen C 1996 J. Soc. Precis. Eng. 18 161
[3] Maksimov A 1997 Ultrasonics 35 79
[4] Landa P S, McClintock P V E 2000 J. Phys. A 33 L433
[5] Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[6] Gitterman M 2001 J. Phys. A 34 L355
[7] Jeyakumari S, Chinnathambi V, Rajasekar S, Sanjuan M A F 2009 Chaos 19 043128
[8] Jeyakumari S, Chinnathambi V, Rajasekar S, Sanjuán M A F 2009 Phys. Rev. E 80 046608
[9] Lin M, Huang Y M 2007 Acta Phys. Sin. 56 6173 (in Chinese) [林敏, 黄咏梅 2007 56 6173]
[10] Lin M, Meng Y 2010 Acta Phys. Sin. 59 3627 (in Chinese) [林敏, 孟莹 2010 59 3627]
[11] Baltanás J P, López L, Blechman I I, Landa P, Zaikin A, Kurths J, Sanjuán M A F 2003 Phys. Rev. E 67 066119
[12] Ullner E, Zaikin A, García-Ojalvo J, Báscones R, Kurths J 2003 Phys. Lett. A 312 348
[13] Deng B, Wang J, Wei X 2009 Chaos 19 013117
[14] Deng B, Wang J, Wei X, Tsang K M, Chan W L 2010 Chaos 20 013113
[15] Yang J H, Liu X B 2010 J. Phys. A 43 122001
[16] Yao C, Zhan M 2010 Phys. Rev. E 81 061129
[17] Yang D X, Hu N Q 2003 J. Natl. Univ. Def. Technol. 25 91 (in Chinese) [杨定新, 胡茑庆 2003 国防科技大学学报 25 91]
[18] Yang J H, Liu X B 2010 Chaos 20 033124
[19] Yang J H, Liu X B 2010 Phys. Scr. 82 025006 010505-7
-
[1] Knoblauch A, Palm G 2005 BioSystems 79 83
[2] Su D, Chiu M, Chen C 1996 J. Soc. Precis. Eng. 18 161
[3] Maksimov A 1997 Ultrasonics 35 79
[4] Landa P S, McClintock P V E 2000 J. Phys. A 33 L433
[5] Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[6] Gitterman M 2001 J. Phys. A 34 L355
[7] Jeyakumari S, Chinnathambi V, Rajasekar S, Sanjuan M A F 2009 Chaos 19 043128
[8] Jeyakumari S, Chinnathambi V, Rajasekar S, Sanjuán M A F 2009 Phys. Rev. E 80 046608
[9] Lin M, Huang Y M 2007 Acta Phys. Sin. 56 6173 (in Chinese) [林敏, 黄咏梅 2007 56 6173]
[10] Lin M, Meng Y 2010 Acta Phys. Sin. 59 3627 (in Chinese) [林敏, 孟莹 2010 59 3627]
[11] Baltanás J P, López L, Blechman I I, Landa P, Zaikin A, Kurths J, Sanjuán M A F 2003 Phys. Rev. E 67 066119
[12] Ullner E, Zaikin A, García-Ojalvo J, Báscones R, Kurths J 2003 Phys. Lett. A 312 348
[13] Deng B, Wang J, Wei X 2009 Chaos 19 013117
[14] Deng B, Wang J, Wei X, Tsang K M, Chan W L 2010 Chaos 20 013113
[15] Yang J H, Liu X B 2010 J. Phys. A 43 122001
[16] Yao C, Zhan M 2010 Phys. Rev. E 81 061129
[17] Yang D X, Hu N Q 2003 J. Natl. Univ. Def. Technol. 25 91 (in Chinese) [杨定新, 胡茑庆 2003 国防科技大学学报 25 91]
[18] Yang J H, Liu X B 2010 Chaos 20 033124
[19] Yang J H, Liu X B 2010 Phys. Scr. 82 025006 010505-7
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