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Combined action of time-delay and colored cross-associated multiplicative and additive noises on stability and stochastic resonance for a stochastic metapopulation system

  • Kang-Kang Wang
  • De-Cai Zong
  • Ya-Jun Wang
  • Sheng-Hong Li
Regular Article

Abstract

In this paper, the transition between the stable state of a big density and the extinction state and stochastic resonance (SR) for a time-delayed metapopulation system disturbed by colored cross-correlated noises are investigated. By applying the fast descent method, the small time-delay approximation and McNamara and Wiesenfeld’s SR theory, we investigate the impacts of time-delay, the multiplicative, additive noises and colored cross-correlated noise on the SNR and the shift between the two states of the system. Numerical results show that the multiplicative, additive noises and time-delay can all speed up the transition from the stable state to the extinction state, while the correlation noise and its correlation time can slow down the extinction process of the population system. With respect to SNR, the multiplicative noise always weakens the SR effect, while noise correlation time plays a dual role in motivating the SR phenomenon. Meanwhile, time-delay mainly plays a negative role in stimulating the SR phenomenon. Conversely, it could motivate the SR effect to increase the strength of the cross-correlation noise in the SNR-β plot, while the increase of additive noise intensity will firstly excite SR, and then suppress the SR effect.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 224 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    Y. Jia, S.N. Yu, J.R. Li, Phys. Rev. E 62, 1869 (2000)ADSCrossRefGoogle Scholar
  3. 3.
    Y. Jia, X.P. Zheng, X.M. Hu, J.H. Li, Phys. Rev. E 63, 031107 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    D. Wu, S.Q. Zhu, Phys. Lett. A 363, 202 (2007)ADSCrossRefGoogle Scholar
  5. 5.
    R. Benzi, A. Sutera, A. Vulpiani, J. Phys. A 14, L453 (1981)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, Tellus 34, 10 (1982)ADSCrossRefGoogle Scholar
  7. 7.
    R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, SIAM J. Appl. Math. 43, 565 (1983)MathSciNetCrossRefGoogle Scholar
  8. 8.
    C.H. Zeng, X.F. Zhou, S.F. Tao, J. Phys. A 42, 495002 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    C.H. Zeng, H. Wang, J. Stat. Phys. 141, 889 (2010)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    C.H. Zeng, C. Zhang, J.K. Zeng, R.F. Liu, H. Wang, J. Stat. Mech. 08, P08027 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    T. Yang et al., Indian J. Phys. 88, 1211 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    T. Yang, Q.L. Han, C.H. Zeng, H. Wang, Y.C. Fu, C. Zhang, Cent. Eur. J. Phys. 12, 383 (2014)Google Scholar
  13. 13.
    C.H. Zeng, Q.L. Han, T. Yang, H. Wang, Z.L. Jia, J. Stat. Mech. 10, 10017 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
    J.M.G. Vilar, J.M. Rubí, Phys. Rev. Lett. 78, 2882 (1997)ADSCrossRefGoogle Scholar
  15. 15.
    R. Rozenfeld, J.A. Freund, A. Neiman, L. Schimansky-Geier, Phys. Rev. E 64, 051107 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    L.C. Du, D.C. Mei, J. Stat. Mech. 11, 11020 (2008)CrossRefGoogle Scholar
  17. 17.
    L.Q. Han et al., Physica A 408, 96 (2014)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    N.G. Stocks, Phys. Rev. E 63, 041114 (2001)ADSCrossRefGoogle Scholar
  19. 19.
    N.G. Stocks, Phys. Lett. A 279, 308 (2000)ADSCrossRefGoogle Scholar
  20. 20.
    P.I. Goychuk, P. Hanggi, Phys. Rev. E 59, 5137 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    P.S. Burada, G. Schmid, D. Reguera, M.H. Vainstein, J.M. Rubi, P. Hänggi, Phys. Rev. Lett. 101, 130602 (2008)ADSCrossRefGoogle Scholar
  22. 22.
    P.S. Burada, G. Schmid, D. Reguera, J.M. Rubi, P. Hänggi, Europhys. Lett. 87, 50003 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    Z. Hou, L. Yang, X. Zuo, H. Xin, Phys. Rev. Lett. 81, 2854 (1998)ADSCrossRefGoogle Scholar
  24. 24.
    P.K. Ghosh, F. Marchesoni, S.E. Savelev, F. Nori, Phys. Rev. Lett. 104, 020601 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    M. Perc, Phys. Rev. E 76, 066203 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    M. Perc, M. Gosak, New J. Phys. 10, 053008 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    C.H. Zeng, Phys. Scr. 81, 025009 (2010)ADSCrossRefGoogle Scholar
  28. 28.
    C.H. Zeng, C.W. Xie, Chin. Phys. Lett. 25, 1587 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    M. Perc, Eur. Phys. J. B 69, 147 (2009)ADSCrossRefGoogle Scholar
  30. 30.
    F. Moss, L.M. Ward, W.G. Sannita, Clin. Neurophys. 115, 267 (2004)CrossRefGoogle Scholar
  31. 31.
    C. Blomberg, Phys. Life Rev. 31, 33 (2006)Google Scholar
  32. 32.
    L.L. Jiang, X.Q. Luo, D. Wan, S.Q. Zhu, Chin. Phys. B 21, 090503 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    D. Valenti, A. Fiasconaro, B. Spagnolo, Physica A 331, 477 (2004)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    B. Spagnolo, A.L. Barbera, Physica A 315, 114 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    L.S. Tsimring, A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001)ADSCrossRefGoogle Scholar
  36. 36.
    C. Masoller, Phys. Rev. Lett. 90, 020601 (2003)ADSCrossRefGoogle Scholar
  37. 37.
    J.C. Cai, D.C. Mei, Mod. Phys. Lett. B 22, 2759 (2008)ADSCrossRefGoogle Scholar
  38. 38.
    D. Huber, L.S. Tsimring, Phys. Rev. Lett. 91, 260601 (2003)ADSCrossRefGoogle Scholar
  39. 39.
    M.C. Mackey, L. Glass, Science 197, 287 (1977)ADSCrossRefGoogle Scholar
  40. 40.
    P.C. Bressoff, S. Coombes, Phys. Rev. Lett. 78, 4665 (1997)ADSCrossRefGoogle Scholar
  41. 41.
    J. Garcia-Ojalvo, R. Roy, Phys. Lett. A 224, 51 (1996)ADSCrossRefGoogle Scholar
  42. 42.
    C. Masoller, Phys. Rev. Lett. 86, 2782 (2001)ADSCrossRefGoogle Scholar
  43. 43.
    L.S. Tsimring, A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001)ADSCrossRefGoogle Scholar
  44. 44.
    X.J. Tian, X.P. Zhang, F. Liu, W. Wang, Phys. Rev. E 80, 011926 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    P. Hänggi, P. Jung, C. Zerbe, F. Moss, J. Stat. Phys. 70, 25 (1993)ADSCrossRefGoogle Scholar
  46. 46.
    R. Levins, Bull. Entomol. Soc. Am. 15, 237 (1998)Google Scholar
  47. 47.
    R. Levins, Lect. Notes Math. 2, 75 (1970)Google Scholar
  48. 48.
    A. Moilanen, I. Hanski, Ecology 79, 2503 (1998)CrossRefGoogle Scholar
  49. 49.
    A. Hastings, S. Harrison, Ann. Rev. Ecol. Syst. 25, 167 (1994)CrossRefGoogle Scholar
  50. 50.
    S. Harrison, Biol. J. Linn. Soc. 42, 73 (1991)CrossRefGoogle Scholar
  51. 51.
    P. Hänggi, P. Jung, Adv. Chem. Phys. 89, 239 (1995)ADSGoogle Scholar
  52. 52.
    I. Hanski, T. Pakkala, M. Kuussaari, G. Lei, Oikos 72, 21 (1995)CrossRefGoogle Scholar
  53. 53.
    L.R. Nie, D.C. Mei, Phys. Lett. A 371, 111 (2007)ADSCrossRefGoogle Scholar
  54. 54.
    I. Hanski, D. Simberloff, in The Metapopulation Approach, its History, Conceptual Domain and Application to Conservation (Academic Press, London, 1997), pp. 5–26Google Scholar
  55. 55.
    S. Harrison, Biol. J. Linn. Soc. 42, 73 (1991)CrossRefGoogle Scholar
  56. 56.
    O. Ovaskainen, K. Sato, J. Bascompte, I. Hanski, J. Theor. Biol. 215, 95 (2002)CrossRefGoogle Scholar
  57. 57.
    J. Bascompte, J. Theor. Biol. 209, 373 (2001)CrossRefGoogle Scholar
  58. 58.
    I.A. Hanski, J. Animal Ecol. 63, 151 (1994)CrossRefGoogle Scholar
  59. 59.
    E.A. Novikov, Sov. Phys. J. Exp. Theor. Phys. 20, 1290 (1964)Google Scholar
  60. 60.
    R.F. Fox, Phys. Rev. A 34, 4525 (1986)ADSMathSciNetCrossRefGoogle Scholar
  61. 61.
    P. Hänggi, Z. Phys. B 31, 407 (1978)ADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    P. Hänggi, F. Marchesoni, P. Grigolini, Z. Phys. B 56, 333 (1984)ADSCrossRefGoogle Scholar
  63. 63.
    P. Hänggi, Colored Noise in Continuous Dynamical Systems: A Functional Calculus Approach, in Noise in Nonlinear Dynamical Systems, edited by F. Moss, P.V.E. McClintock (Cambridge University Press, 1989), Vol. 1, Chap. 9, pp. 307–328Google Scholar
  64. 64.
    P. Hänggi, P. Jung, Adv. Chem. Phys. 89, 239 (1995)ADSGoogle Scholar
  65. 65.
    B. McNamara, K. Wiesenfeld, Phys. Rev. A 39, 4854 (1989)ADSCrossRefGoogle Scholar
  66. 66.
    P. Jung, P. Hänggi, Phys. Rev. A 44, 8032 (1991)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Kang-Kang Wang
    • 1
  • De-Cai Zong
    • 2
  • Ya-Jun Wang
    • 1
  • Sheng-Hong Li
    • 3
  1. 1.School of Mathematics and Physics, Jiangsu University of Science and TechnologyZhenjiangP.R. China
  2. 2.College of Computer Science and Engineering, Changshu Institute of TechnologyChangshuP.R. China
  3. 3.College of Mathematics, Nanjing Normal UniversityNanjingP.R. China

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