Skip to main content
SpringerLink
Log in

Phase transitions induced by time-delay and different noises

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The effects of global and local time-delay on a genotype selection model driven by colored or sine-Wiener noise are investigated. The stationary probability distributions are derived by simulating the Langevin Equation directly. It is found that compared to the colored noise, the bounded noise can enhance transitions, though they have the same mean and stationary correlation. Local time-delay and the global one have opposite role in the system with different noises. When time-delay is global, neither the colored noise nor the sine-Wiener noise can induce phase transitions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Hirsch, J.E., Huberman, B.A., Scalapino, D.J.: Theory of intermittency. Phys. Rev. A 25, 519–532 (1982)

    Article  Google Scholar 

  2. Mantegna, R.N., Spagnolo, B.: Noise enhanced stability in an unstable system. Phys. Rev. Lett. 76, 563–566 (1996)

    Article  Google Scholar 

  3. Augdov, N.V., Spagnolo, B.: Noise-enhanced stability of periodically. Phys. Rev. E 64, 035102 (2001)

  4. Spagnolo, B., Agudov, N.V., Dubkov, A.A.: Noise enhanced stability. Acta Phys. Pol. B 35, 1419–1436 (2004)

    Google Scholar 

  5. Liu, K.H., Jin, Y.F.: Stochastic resonance in periodic potentials driven by colored noise. Phys. A 392, 5283–5288 (2013)

    Article  MathSciNet  Google Scholar 

  6. Dong, X.J., Yan, A.J.: Stochastic resonance in a linear static system driven by correlated multiplicative and additive noises. Appl. Math. Model. 38, 2915–2921 (2014)

    Article  MathSciNet  Google Scholar 

  7. Toshiya, I.: Study of stochastic resonance by method of stochastic energetics. Phys. A 300, 350–358 (2001)

    Article  MATH  Google Scholar 

  8. Ning, L.J., Xu, W.: Stochastic resonance in linear system driven by multiplicative and additive noise. Phys. A 382, 415–422 (2007)

    Article  Google Scholar 

  9. Xu, Y., Feng, J., Feng, J.J., Zh, H.Q.: Stochastic bifurcation for a tumor-immune system with symmetric Levy noise. Phys. A 392, 4739–4748 (2013)

    Article  MathSciNet  Google Scholar 

  10. Yu, S.N., Jia, Y.: Noise-induced transition in a Fizhugh-Nagumo neural model. J. Cent. China Norm. Univ. (Nat. Sci.) 34, 281–284 (2000)

  11. Gudyma, I., Maksymov, A., Dimian, M.: Stochastic kinetics of photoinduced phase transitions in spin-crossover solids. Phys. Rev. E 88, 042111 (2013)

  12. Arnold, L., Horsthemke, W., Lefever, R.: White and coloured external noise and transition phenomena in nonlinear systems. Z. Phys. B 29, 367–373 (1978)

    Article  Google Scholar 

  13. Soldatov, A.V.: Purely noise-induced phase transition in the model of gene selection with colored noise term. Mod. Phys. Lett. B 7, 1253–1261 (1993)

    Article  Google Scholar 

  14. Zhang, L., Cao, L.: Effect of correlated noises in a genetic model. Chin. Phys. Lett. 27, 060504 (2010)

  15. Castro, F., Sanchez, A.D., Wio, H.S.: Reentrance phenomenta in noise induced transitions. Phys. Rev. Lett. 75, 1691–1694 (1995)

    Article  Google Scholar 

  16. Wang, C.J., Mei, D.C.: Transitions in a genotype selection model driven by coloured noises. Chin. Phys. B 17, 479–485 (2008)

  17. Fei, L., Wei, G., Mei, D.C.: Stochastic resonance induced by bounded noise and periodic signal in an asymmetric bistable system. Phys. A 391, 5305–5310 (2012)

    Article  Google Scholar 

  18. Wei, G., Du L.C., Mei, D.C.: Transitions induced by time delays and cross-correlated sine-Wiener noises in a tumor-immune system interplay. Phys. A 391, 1270–1280 (2012)

  19. d’Onofrio, A.: Bounded-noise-induced transitions in a tumor-immune system interplay. Phys. Rev. E 81, 021923 (2010)

  20. Bobryk, R.V., Chrzeszczyk, A.: Transitions induced by bounded noise. Phys. A 358, 263–272 (2005)

    Article  Google Scholar 

  21. Wang, C.J.: Time-delay effect of a stochastic genotype selection model. Acta Phys. Sin. 5, 050501 (in Chinese) (2012)

  22. Du, L.C., Mei, D.C.: Stochastic resonance in a bistable system with global delay and two noises. Eur. Phys. J. B 85, 1–5 (2012)

    Article  Google Scholar 

  23. Gu, X., Zhu, S., Wu, D.: Two different kinds of time delays in a stochastic system. Eur. Phys. J. D 42, 461–466 (2007)

    Article  Google Scholar 

  24. Sancho, J.M., San Miguel, M., Katz, S.L., Gunton, J.D.: Analytical and numerical studies of multiplicative noise. Phys. Rev. A 26, 1589–1609 (1982)

    Article  Google Scholar 

  25. Desmond, J.H.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43, 525–546 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China under Grant Nos. 11202120 and 61273311, the Fundamental Research Funds for the Central Universities under No. GK201502007.

Author information

Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, People’s Republic of China

    H. Yang & L. J. Ning

Authors
  1. H. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. J. Ning
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. J. Ning.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, H., Ning, L.J. Phase transitions induced by time-delay and different noises. Nonlinear Dyn 88, 2427–2433 (2017). https://doi.org/10.1007/s11071-017-3387-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3387-3

Keywords

Search

Navigation