Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

Chunyan Bai, Luchun Du 1 , and Dongcheng Mei 1
  • 1 Department of Physics, Yunnan University, Kunming, 650091, China
  • 2 Department of Computer Science, Simao Teachers College, Puer, 665000, China

Abstract

The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] R. Benzi, A. Sutera, A. Vulpiani, J. Phys. A-Math. Gen. 14, L453 (1981) http://dx.doi.org/10.1088/0305-4470/14/11/006

  • [2] R. Benzi, A. Sutera, A. Vulpiani, Tellus 34, 10 (1982) http://dx.doi.org/10.1111/j.2153-3490.1982.tb01787.x

  • [3] C. Nicolis, G. Nicolis, Tellus 33, 225 (1981) http://dx.doi.org/10.1111/j.2153-3490.1981.tb01746.x

  • [4] C. Nicolis, Tellus 34, 1 (1982) http://dx.doi.org/10.1111/j.2153-3490.1982.tb01786.x

  • [5] C. Nicolis, G. Nicolis, G. Hu, Phys. Lett. A 151, 139 (1990) http://dx.doi.org/10.1016/0375-9601(90)90180-V

  • [6] S. Fauve, F. Heslot, Phys. Lett. A 97, 5 (1983) http://dx.doi.org/10.1016/0375-9601(83)90086-5

  • [7] B. McNamara, K. Wiesenfeld, R. Roy, Phys. Rev. Lett. 60, 2626 (1988) http://dx.doi.org/10.1103/PhysRevLett.60.2626

  • [8] B. McNamara, K. Wiesenfeld, Phys. Rev. A 39, 4854 (1989) http://dx.doi.org/10.1103/PhysRevA.39.4854

  • [9] M. I. Dykman, R. Mannella, P. V. E. McClintock, N. G. Stocks, Phys. Rev. Lett. 65, 48 (1990) http://dx.doi.org/10.1103/PhysRevLett.65.48

  • [10] M. I. Dykman, R. Mannella, P. V. E. McClintock, N. G. Stocks, Phys. Rev. Lett. 65, 2606 (1990) http://dx.doi.org/10.1103/PhysRevLett.65.2606

  • [11] C. Presilla, F. Marchesoni, L. Gammaitoni, Phys. Rev. A 40, 2105 (1989) http://dx.doi.org/10.1103/PhysRevA.40.2105

  • [12] L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, S. Santucci, Phys. Rev. Lett. 62, 349 (1989) http://dx.doi.org/10.1103/PhysRevLett.62.349

  • [13] T. Zhou, F. Moss, Phys. Rev. A 41, 4255 (1990) http://dx.doi.org/10.1103/PhysRevA.41.4255

  • [14] T. Zhou, F. Moss, P. Jung, Phys. Rev. A 42, 3161 (1990) http://dx.doi.org/10.1103/PhysRevA.42.3161

  • [15] L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998) http://dx.doi.org/10.1103/RevModPhys.70.223

  • [16] J. H. Li, Phys. Rev. E 66, 031104 (2002) http://dx.doi.org/10.1103/PhysRevE.66.031104

  • [17] J. M. G. Vilar, J. M. Rubi, Phys. Rev. Lett. 78, 2882 (1997) http://dx.doi.org/10.1103/PhysRevLett.78.2882

  • [18] J. H. Li, Phys. Rev. E 76, 021113 (2007) http://dx.doi.org/10.1103/PhysRevE.76.021113

  • [19] J. H. Li, Y. X. Han, Phys. Rev. E 74, 051115 (2006) http://dx.doi.org/10.1103/PhysRevE.74.051115

  • [20] V. Barzykin, K. Seki, Europhys. Lett. 57, 6555 (1997)

  • [21] A. Fulinski, R. F. Góra, Phys. Rev. E 64, 011905 (2001) http://dx.doi.org/10.1103/PhysRevE.64.011905

  • [22] A. A. Zaikin, J. Kurths, L. Schimansky-Geier, Phys. Rev. Lett. 85, 227 (2000) http://dx.doi.org/10.1103/PhysRevLett.85.227

  • [23] J. J. Collins, C. C. Chow, A. C. Capela, T. T. Lmhoff, Phys. Rev. E 54, 5575 (1996) http://dx.doi.org/10.1103/PhysRevE.54.5575

  • [24] C. Nicolis, G. Nicolis, New J. Phys. 7, 8 (2005) http://dx.doi.org/10.1088/1367-2630/7/1/008

  • [25] C. Nicolis, G. Nicolis, Phys. Rev. E 62, 197 (2000) http://dx.doi.org/10.1103/PhysRevE.62.197

  • [26] P. F. Verhulst, Correspondance Mathematique et Physique 10, 113 (1838)

  • [27] R. A. Fisher, Annals of Eugenics 7, 353 (1937)

  • [28] A. Kolomogoroff, I. Petrovsky, N. Piscounoff, MoscowUniversity Bulletin of Mathematics (in English) 1, 1 (1937)

  • [29] M. Eigen, P. Schuster, The Hypercycle: A Principle of Natural Self-Organization (Springer, Berlin, 1979)

  • [30] F. G. Li, Cent. Eur. J. Phys. 6, 539 (2008) http://dx.doi.org/10.2478/s11534-008-0089-y

  • [31] H. Krug, G. Taubert, Arch. Geschwulstforsch. 55, 235 (1985)

  • [32] B. Q. Ai et al., Phys. Rev. E 67, 022903 (2003) http://dx.doi.org/10.1103/PhysRevE.67.022903

  • [33] D. C. Mei, C. W. Xie, L. Zhang, Eur. Phys. J. B 41, 107 (2004) http://dx.doi.org/10.1140/epjb/e2004-00300-1

  • [34] C. J. Wang, Q. Wei, D. C. Mei, Mod. Phys. Lett. B 21, 789 (2007) http://dx.doi.org/10.1142/S0217984907013225

  • [35] L. B. Han et al., Chin. Phys. Lett. 24, 632 (2007) http://dx.doi.org/10.1088/0256-307X/24/3/013

  • [36] C. J. Wang, Q. Wei, D. C. Mei, Phys. Lett. A 372, 2176 (2008) http://dx.doi.org/10.1016/j.physleta.2007.11.040

  • [37] J. C. Cai, C. J. Wang, D. C. Mei, Chin. Phys. Lett. 24, 1162 (2007) http://dx.doi.org/10.1088/0256-307X/24/5/010

  • [38] A. Caruso, M. E. Gargano, D. Valenti, A. Fiasconaro, B. Spagnolo, Fluct. Noise Lett. 5, L349 (2005) http://dx.doi.org/10.1142/S0219477505002768

  • [39] C. W. Gardiner, Handbook of Stochastic Methods, Springer Series in Synergetics Vol. 13 (Springer-Verlag, Berlin, 1983)

  • [40] P. Hänggi, F. Marchesoni, P. Grigolini, Z. Phys. B Con. Mat. 56, 333 (1984) http://dx.doi.org/10.1007/BF01306642

  • [41] E. Guardia, M. S. Miguel, Phys. Lett. A 109, 9 (1985) http://dx.doi.org/10.1016/0375-9601(85)90380-9

  • [42] R. F. Fox, Phys. Rev. A 33, 467 (1986) http://dx.doi.org/10.1103/PhysRevA.33.467

  • [43] A. J. R. Madureira, P. Hänggi, H. S. Wio, Phys. Lett. A 217, 248 (1996) http://dx.doi.org/10.1016/0375-9601(96)00345-3

OPEN ACCESS

Journal + Issues

Search