Skip to main content
SpringerLink
Log in

Bursting and delay behavior in the Belousov-Zhabotinsky reaction with external excitation

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

The dynamics of a typical Belousov-Zhabotinsky (BZ) reaction with two time scales and low perturbation frequency is investigated in this paper. For specific parameters, the typical phenomenon called as double-Hopf bursting is observed, and the corresponding generation mechanism is presented based on the slow-fast dynamical analysis method. With the decrease of the amplitude of external excitation, the double-Hopf bursting evolves into a single-Hopf one. Furthermore, periodic bifurcation delay behaviors are found when the time-varying parameter slowly passes through the critical point of Hopf bifurcation, which results into spiking state (SP) delay behaviors. The detailed delay phenomena as well as their mechanisms are exhibited by theoretical analysis and numerical simulation.

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

Similar content being viewed by others

References

  1. Q.S. Lu, Z. Yang, L.X. Duan et al., Chaos, Solitons Fractals 40, 577 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  2. Q.S. Bi, Sci. China Technol. Sci. 53, 748 (2010)

    Article  Google Scholar 

  3. G.V. Savino, C.M. Formigli, Bio Syst. 97, 9 (2009)

    Google Scholar 

  4. A. Vidal, Lect. Notes Control Inf. Sci. 341, 439 (2006)

    Article  Google Scholar 

  5. Q.Y. Wang, H.H. Zhang, M. Perc et al., Commun. Nonlinear Sci. Numer. Simul. 17, 3979 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  6. S.P. Yang, Y.J. Shen, Chaos, Solitons Fractals 40, 1808 (2009)

    Article  ADS  Google Scholar 

  7. Y.J. Shen, S.P. Yang, X.D. Liu, Int. J. Mech. Sci. 48, 1256 (2006)

    Article  Google Scholar 

  8. Y.J. Shen, S.P. Yang, C.Z. Pan, X.D. Liu, J. Low Freq. Noise, Vib. Active Control 23, 179 (2004)

    Article  Google Scholar 

  9. H. Ding, J. Sound Vib. 353, 308 (2015)

    Article  ADS  Google Scholar 

  10. J. Rinzel, Lect. Notes Math. 1151, 304 (1985)

    Article  Google Scholar 

  11. N.F. Rulkov, Phys. Rev. E 65, 041922 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Perc, M. Marhl, Chaos, Solitons Fractals 18, 759 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  13. T. Hongray, J. Balakrishnan, S.K. Dana, Chaos 25, 123104 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  14. Z.D. Zhang, B.B. Liu, Q.S. Bi, Nonlinear Dyn. 79, 195 (2014)

    Article  Google Scholar 

  15. X.H. Li, Q.S. Bi, Chin. Phys. Lett. 30, 070503 (2013)

    Article  ADS  Google Scholar 

  16. Q.S. Lu, Z.Q. Yang, L.X. Duan et al., Chaos, Solitons Fractals 40, 577 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  17. X.H. Li, J.Y. Hou, Int. J. Non-Linear Mech. 81, 165 (2016)

    Article  ADS  Google Scholar 

  18. S.M. Baer, T. Erneux, J. Rinzel, Siam J. Appl. Math. 49, 55 (1989)

    Article  MathSciNet  Google Scholar 

  19. L. Holden, T. Erneux, Siam J. Appl. Math. 53, 1045 (1993)

    Article  MathSciNet  Google Scholar 

  20. X.J. Han, Q.S. Bi, C. Zhang et al., Nonlinear Dyn. 77, 1285 (2014)

    Article  Google Scholar 

  21. F. Rossi, M.A. Budroni, N. Marchettini et al., Chem. Phys. Lett. 480, 322 (2009)

    Article  ADS  Google Scholar 

  22. N.B. Ganaie, G.M. Peerzada, J. Braz. Chem. Soc. 20, 1262 (2009)

    Article  Google Scholar 

  23. N.B. Ganaie, G.M. Peerzada, Int. J. Chem. Kin. 41, 650 (2009)

    Article  Google Scholar 

  24. Y. Hara, Y. Takenaka, Sensors 14, 1497 (2014)

    Article  Google Scholar 

  25. J. Ren, M. Yao, G. Zhang et al., J. Polym. Res. 22, 197 (2015)

    Article  Google Scholar 

  26. J. Ren, M. Yao, G. Zhang et al., J. Polym. Res. 22, 1 (2015)

    Article  Google Scholar 

  27. K. Bar-Eli, R.M. Noyes, J. Chem. Phys. 86, 1927 (1987)

    Article  ADS  Google Scholar 

  28. L. Györgyi, R.J. Field, J. Chem. Phys. 91, 6131 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  29. X.L. Wang, Y. Chang, D.S. Xu, Int. J. Bifurc. Chaos 25, 1550093 (2015)

    Article  Google Scholar 

  30. P.E. Strizhak, A.L. Kawczynski, J. Phys. Chem. 99, 10830 (1995)

    Article  Google Scholar 

  31. V.K. Vanag, A.M. Zhabotinsky, I.R. Epstein, Phys. Rev. Lett. 86, 552 (2001)

    Article  ADS  Google Scholar 

  32. L. Yang, M. Dolnik, A.M. Zhabotinsky et al., Phys. Rev. E 62, 6414 (2000)

    Article  ADS  Google Scholar 

  33. A. Cadena, D. Barragán, Jesús Ágreda, J. Braz. Chem. Soc. 24, 2028 (2013)

    Google Scholar 

  34. Q.S. Bi, Sci. China Technol. Sci. 53, 748 (2010)

    Article  Google Scholar 

  35. X.H. Li, Q.S. Bi, Chin. Phys. Lett. 30, 10503 (2013)

    Article  Google Scholar 

  36. T. Sekiguchi, Y. Mori, I. Hanazaki, Chem. Lett. 1993, 1309 (1993)

    Article  Google Scholar 

  37. K. Agladze, S. Obata, K. Yoshikawa, Physica D 84, 238 (1995)

    Article  ADS  Google Scholar 

  38. C.M. Bender, S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China

    Jingyu Hou, Xianghong Li & Dawei Zuo

  2. Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang, China

    Yingna Li

Authors
  1. Jingyu Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xianghong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dawei Zuo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yingna Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianghong Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hou, J., Li, X., Zuo, D. et al. Bursting and delay behavior in the Belousov-Zhabotinsky reaction with external excitation. Eur. Phys. J. Plus 132, 283 (2017). https://doi.org/10.1140/epjp/i2017-11550-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2017-11550-5

Search

Navigation