×

Coherence and stochastic resonance in a periodic potential driven by multiplicative dichotomous and additive white noise. (English) Zbl 1375.34088

Summary: In this paper, the dynamical analysis of a periodic potential subject to noise without and with the periodic signal is presented. The third-order differential equation of the stationary probability density (SPD) is derived for the periodic potential, which driven by multiplicative dichotomous and additive white noise. It is found that the SPD undergoes a transition from the unimodal to the bimodal structure with the increase of multiplicative noise intensity. The power spectra density (PSD) and the qualify factor show the peak structure when a suitable dose of noise intensity is added. That is, the coherence resonance (CR) appears. Meanwhile, the average input energy per period and the amplitude of average response are calculated to quantify stochastic resonance (SR). The curve of the average input energy per period shows multiple extrema as a function of multiplicative noise intensity at the small fixed additive noise intensity. This phenomenon indicates the stochastic multi-resonance happens for this case.

MSC:

34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Benzi, R.; Sutera, A.; Vulpiani, A., The mechanism of stochastic resonance, J Phys A, 14, L453-L455 (1981)
[2] Gammaitoni, L.; Hänggi, P.; Jung, P.; Marchesoni, F., Stochastic resonance, Rev Mod Phys, 70, 224-260 (1998)
[3] Hu, G.; Ditzinger, T.; Ning, CZ; Haken, H., Stochastic resonance without external periodic force, Phys Rev Lett, 71 (1993), 807-4
[4] McNamara, B.; Wiesenfeld, K., Theory of stochastic resonance, Phys Rev A, 39 (1989), 4854-16
[5] Hu, G.; Nicolis, G.; Nicolis, C., Periodically forced Fokker-Planck equation and stochastic resonance, Phys Rev A, 42 (1990), 2030-12
[6] Dykman, MI; Mannella, R.; McClintock, PVE; Soskin, SM; Stocks, NG, Noise-induced narrowing of peaks in the power spectra of underdamped nonlinear oscillators, Phys Rev A, 42, 7041-7049 (1990)
[7] Zhou, T.; Moss, F.; Jung, P., Escape-time distributions of a periodically modulated bistable system with noise, Phys Rev A, 42 (1990), 3161-10
[8] Kuske, R., Multiple-scales approximation of a coherence resonance route to chatter, Comput Sci Eng, 8, 35-39 (2006)
[9] McInnes, CR; Gorman, DG; Cartmell, MP, Enhanced vibrational energy harvesting using nonlinear stochastic resonance, J Sound Vib, 318, 655-658 (2008)
[10] Laing, CR; Longtin, A., Noise-induced stabilization of bumps in systems with long-range spatial coupling, Physica D, 160 (2001), 149-24 · Zbl 0997.92002
[11] Xu, Y.; Wu, J.; Du, L.; Yang, H., Stochastic resonance in a genetic toggle model with harmonic excitation and Lévy noise, Chaos Solit Fract, 9 (2016), 91-10 · Zbl 1372.92067
[12] Fioretti, A.; Guidoni, L.; Mannella, R.; Arimondo, E., Evidence of stochastic resonance in a laser with saturable absorber: experiment and theory, J Stat Phys, 70, 403-410 (1992)
[13] Fauve, S.; Heslot, F., Stochastic resonance in a bistable system, Phys Lett A, 97 (1983), 5-3
[14] McNamara, B.; Wiesenfeld, K.; Roy, R., Observation of stochastic resonance in a ring laser, Phys Rev Lett, 60 (1988), 2625-5
[15] Santos, GJE; Rivera, M.; Parmananda, P., Experimental evidence of coexisting periodic stochastic resonance and coherence resonance phenomena, Phys Rev Lett, 92, 230601-230604 (2004)
[16] Fronzoni, L.; Mannella, R., Stochastic resonance in periodic potentials, J Stat Phys, 70, 501-512 (1993)
[17] Nie, LR; Mei, DC, The underdamped Josephson junction subjected to colored noises, Eur Phys J B, 58, 475-477 (2007)
[18] Li, JH, Noise-induced multi-decrease and multi-increase of net voltage in Josephson junctions, J Phys: Condens Matter, 22, 115702-115705 (2010)
[19] Saikia, S.; Jayannavar, M.; Mahato, MC, Stochastic resonance in periodic potentials, Phys Rev E, 83, 061121-061129 (2011)
[20] Saikia, S., The role of damping on stochastic resonance in a periodic potential, Phys A, 416 (2014), 411-10
[21] Liu, KH; Jin, YF, Stochastic resonance in periodic potentials driven by colored noise, Phys A, 392, 5283-5286 (2013) · Zbl 1395.82191
[22] Ma, ZM; Jin, YF, Stochastic resonance in periodic potential driven by dichotomous noise, Acta Phys Sin, 64, Article 240502 pp. (2015)
[23] Jin, YF; Xu, W.; Xu, M., Stochastic resonance in an asymmetric bistable system driven by correlated multiplicative and additive noise, Chaos Solit Fract, 26, 1183-1185 (2005) · Zbl 1096.94509
[24] Jin, YF; Hu, HY, Coherence and stochastic resonance in a delayed bistable system, Phys A, 382, 423-427 (2007)
[25] Jin, YF, Noise-induced dynamics in a delayed bistable system with correlated noises, Phys A, 391 (2012), 1928-6
[26] Xu, Y.; Wu, J.; Zhang, HQ; Ma, SJ, Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise, Nonlinear Dyn, 70, 531-539 (2012)
[27] Xu, Y.; Li, JJ; Feng, J.; Zhang, HQ; Xu, W.; Duan, JQ, Lévy noise-induced stochastic resonance in a bistable system, Eur Phys J B, 86 (2013), 198-8 · Zbl 1515.37049
[28] Berthet, R.; Petrossian, A.; Residori, S.; Roman, B.; Fauve, S., Effect of multiplicative noise on parametric instabilities, Phys D, 174 (2003), 84-16 · Zbl 1076.70513
[29] Jin, YF, Delay-independent stability of moments of a linear oscillator with delayed state feedback and parametric white noise, Probab Eng Mech, 41, 115-116 (2015)
[30] Berdichevsky, V.; Gitterman, M., Josephson junction with noise, Phys Rev E, 56 (1997), 6340-15
[31] Gitterman, M., Mean-square displacement of a stochastic oscillator: linear vs quadratic noise, Phys A, 391 (2012), 3033-10
[32] Li, YG; Xu, Y.; Kurths, J.; Yue, XL, Lévy-noise-induced transport in a rough triple-well potential, Phys Rev E, 94 (2016), 042222-10
[33] Barik, D.; Ghosh, PK; Ray, DS, Langevin dynamics with dichotomous noise; direct simulation and applications, J Stat Mech, 3, P03010-P03025 (2006) · Zbl 07080003
[34] Gardiner, CW, Handbook of stochastic methods (1985), Springer-Verlag: Springer-Verlag Berlin
[35] Viterbi, AJ, Principles of coherent communications (1966), McGraw-Hill: McGraw-Hill New York
[36] Shapiro, B.; Gitterman, M.; Dayan, I., Shapiro steps in the fluxon motion in superconductors, Phys Rev B, 46 (1992), 8416-5
[37] Chen, BX; Dong, JM, Thermally assisted vortex diffusion in layered high-Tc superconductors, Phys Rev B, 44 (1991), 10206-5
[38] Doering, CR; Sargsyan, KV; Smereka, PA, Numerical method for some stochastic differential equations with multiplicative noise, Phys Lett A, 344 (2005), 149-7 · Zbl 1194.65024
[39] Sekimoto, K., Stochastic energetic (2010), Springer: Springer Berlin · Zbl 1201.82001
[40] Casado-Pascual, J.; Gómez-Ordóñez, J.; Morillo, M.; Hänggi, P., Rocking bistable systems: use and abuse of linear response theory, Europhys Lett, 58, 342-347 (2002)
[41] Alfonsi, L.; Gammaitoni, L.; Santucci, S.; Bulsara, AR, Intrawell stochastic resonance versus interwell stochastic resonance in underdamped bistable system, Phys Rev E, 62 (2000), 299-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.