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Periodic potential system is widely used in a lot of areas such as biological ratchet model of motor, Josephson junction in the field of physics, engineering mechanics of the damping pendulum model, etc. Meanwhile, in the study of stochastic resonance, noise is crucial for dynamical system evolution. There are mostly colored Gaussian noises with nonzero correlation times in practical problems. Dichotomous noises belong to the color noises, and they have some simple statistical properties. In this paper, we study the motion of a Brownian particle in a periodic potential, driven by both a periodic signal and a dichotomous noise. The periodic potential system is different from the bistable system, so we use multiple indexes to explain the stochastic resonance. We calculate the average input energy of the system and the average output signal amplitude and phase difference by using stochastic energetics. Then we discuss the influences of the dichotomous noise intensity, noise correlation time and asymmetric coefficient of potential energy on the stochastic resonance. The results show that with the increase of the noise correlation time, a minimum value and a maximum value occur on the curve of the average input energy, meanwhile, the phenomenon of resonance appears in the system. With the increase of the noise intensity, the value of noise correlation time becomes greater when the phenomenon of stochastic resonance appears. Therefore, the region of stochastic resonance becomes bigger as the noise intensity or the asymmetry coefficient increases. Moreover, with the increase of the noise intensity, a mono peak is found for the signal-to-noise ratio (SNR) of the system and the stochastic resonance appears in this system. With the increase of the noise intensity, we compare the change of the SNR, the average input energy, and the average output signal amplitude. We find that the values of the amplitudes of the average output signal and SNR are basically the same, while the values of the amplitude of the average input energy of the system are a little different. This is because during the process of periodic signal doing work to the system, noise does work and passive dissipation energy of the system occures. In addition, when the curves of the amplitude of the average output signal and SNR reach their corresponding minimum values, the phase difference between the output signal and input signal is minimal.
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Keywords:
- periodic potential /
- dichotomous noise /
- stochastic resonance /
- stochastic energetics
[1] Benzi R, Sutera A, VtllPiana A 1981 J. Phys. A 14 L453
[2] Nicolis C 1982 Tellus 3 312
[3] Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[4] Murali K, Sinha S, Ditto W L, Bulsara A R 2009 Phys. Rev. Lett. 102 104101
[5] Zhang L Y, Cao L, Wu D J 2003 Acta Phys. Sin. 52 1174 (in Chinese) [张良英, 曹力, 吴大进 2003 52 1174]
[6] Jin Y F, Li B 2014 Acta Phys. Sin. 63 210501 (in Chinese) [靳艳飞, 李贝 2014 63 210501]
[7] Fronzoni L, Mannella R 1993 J. Stat. Phys. 70 501
[8] Dan D, Mahato M C, Jayannavar A M 1999 Phys. Rev. E 60 6421
[9] Saikia S, Jayannavar A M, Mahato M C 2011 Phys. Rev. E 83 061121
[10] Saikia S 2014 Physica A 416 411
[11] Liu K H, Jin Y F 2013 Physica A 392 5283
[12] Ai B Q, Chen Q Y, He Y F, Li F G, Zhong W R 2014 Phys. Rev. E 88 062129
[13] Fulinski A 1997 Acta Phys. Pol. B 28 1811
[14] Fulinski A 1995 Phys. Rev. E 52 4523
[15] Rozenfeld R, Neiman A, Schimansky G L 2000 Phys. Rev. E 62 3031
[16] Wozinski A 2006 Acta Phys. Pol. B 37 1677
[17] Xu Y, Wu J, Zhang H Q, Ma S J 2012 Nonlinear Dyn. 70 531
[18] Jin Y F 2015 Chin. Phys. B 24 060502
[19] Jin Y F, Xu W, Li W, Xu M 2005 J. Phys. A 38 3733
[20] Barik D, Ghosh P K, Ray D S 2006 J. Stat. Mech. 3 03010
[21] Xu Y, Jin X Q, Zhang H Q, Yang T T 2013 J. Stat. Phys. 152 753
[22] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) p221 (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221页]
[23] Kang Y M, Xu J X, Xie Y 2003 Acta Phys. Sin. 52 802 (in Chinese) [康艳梅, 徐健学, 谢勇 2003 52 802]
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[1] Benzi R, Sutera A, VtllPiana A 1981 J. Phys. A 14 L453
[2] Nicolis C 1982 Tellus 3 312
[3] Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[4] Murali K, Sinha S, Ditto W L, Bulsara A R 2009 Phys. Rev. Lett. 102 104101
[5] Zhang L Y, Cao L, Wu D J 2003 Acta Phys. Sin. 52 1174 (in Chinese) [张良英, 曹力, 吴大进 2003 52 1174]
[6] Jin Y F, Li B 2014 Acta Phys. Sin. 63 210501 (in Chinese) [靳艳飞, 李贝 2014 63 210501]
[7] Fronzoni L, Mannella R 1993 J. Stat. Phys. 70 501
[8] Dan D, Mahato M C, Jayannavar A M 1999 Phys. Rev. E 60 6421
[9] Saikia S, Jayannavar A M, Mahato M C 2011 Phys. Rev. E 83 061121
[10] Saikia S 2014 Physica A 416 411
[11] Liu K H, Jin Y F 2013 Physica A 392 5283
[12] Ai B Q, Chen Q Y, He Y F, Li F G, Zhong W R 2014 Phys. Rev. E 88 062129
[13] Fulinski A 1997 Acta Phys. Pol. B 28 1811
[14] Fulinski A 1995 Phys. Rev. E 52 4523
[15] Rozenfeld R, Neiman A, Schimansky G L 2000 Phys. Rev. E 62 3031
[16] Wozinski A 2006 Acta Phys. Pol. B 37 1677
[17] Xu Y, Wu J, Zhang H Q, Ma S J 2012 Nonlinear Dyn. 70 531
[18] Jin Y F 2015 Chin. Phys. B 24 060502
[19] Jin Y F, Xu W, Li W, Xu M 2005 J. Phys. A 38 3733
[20] Barik D, Ghosh P K, Ray D S 2006 J. Stat. Mech. 3 03010
[21] Xu Y, Jin X Q, Zhang H Q, Yang T T 2013 J. Stat. Phys. 152 753
[22] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) p221 (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221页]
[23] Kang Y M, Xu J X, Xie Y 2003 Acta Phys. Sin. 52 802 (in Chinese) [康艳梅, 徐健学, 谢勇 2003 52 802]
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