Bulletin of the Korean Chemical Society

Korean Chemical Society (대한화학회)
권호 표지
DOI QR코드

DOI QR Code

Effects of Noise on a Model of Oscillatory Chemical Reaction

  • Basavaraja, C. (Department of Chemistry and Institute of Functional Materials, Inje University) ;
  • Bagchi, Biman (Solid State and Structural Chemistry Unit, Indian Institute of Science) ;
  • Park, Do-Young (Department of Chemistry and Institute of Functional Materials, Inje University) ;
  • Choi, Young-Min (Department of Chemistry and Institute of Functional Materials, Inje University) ;
  • Park, Hyun-Tae (Department of Chemistry and Institute of Functional Materials, Inje University) ;
  • Choe, Sang-Joon (Department of Chemistry and Institute of Functional Materials, Inje University) ;
  • Huh, Do-Sung (Department of Chemistry and Institute of Functional Materials, Inje University)
  • Published : 2006.10.20
Download PDF
⟨ Previous Next ⟩

Abstract

A simple oscillating reaction model subject to additive Gaussian white noise is investigated as the model is located in the dynamic region of oscillations. The model is composed of three ordinary differential equations representing the time evolutions of X, Y, and Z, respectively. Initially, a uniform random noise is separately added to the three equations to study the effect of noise on the oscillatory cycle of X, Y, and Z. For a given value of noise intensity, the amplitude of oscillation increases monotonically with time. Furthermore, the noise is added to any one of the three equations to study the impact of noise on one species on the bifurcation behavior of the other.

Keywords

References

  1. Linder, B.; Ojalvo, J. G.; Neiman, A.; Geirr, L. S. Phys. Rep. 2004, 392, 312
  2. Miyakawa, K.; Tanaka, T.; Isikawa, H. Phys. Rev. E 2003, 67, 066206 https://doi.org/10.1103/PhysRevE.67.066206
  3. Zhu, R.; Shu, Li. Q. Phys. Chem. Chem. Phys. 2002, 4, 82 https://doi.org/10.1039/b106072b
  4. Zhdanov, V. P. Phys. Chem. Chem. Phys. 2001, 3, 1432 https://doi.org/10.1039/b100192m
  5. Kostur, M.; Schimansky-Geier, L. Phys. Lett. A 2000, 265, 337 https://doi.org/10.1016/S0375-9601(99)00906-8
  6. Denisov, S. L.; Horsthemke, W. Phys. Rev. E 2002, 65, 061109-1 https://doi.org/10.1103/PhysRevE.65.061109
  7. Horsthemke, W. Phys. Lett. A 1999, 263, 285 https://doi.org/10.1016/S0375-9601(99)00711-2
  8. Pikovsky, A. S.; Kurths, J. Phys. Rev. Lett. 1997, 78, 775 https://doi.org/10.1103/PhysRevLett.78.775
  9. Horsthemke, W.; Lefever, R. Noise Induced Transitions; Springer; Berlin, 1984; Vol. 1, p 530
  10. Gardiner, C. W. Handbook of Stochastic Methods; Springer: Berlin, 1985; p 1
  11. Segeti, D.; Horsthemke, W. J. Stat. Phys. 1989, 54, 1217 https://doi.org/10.1007/BF01044713
  12. Kostur, M. Fluct. Noise. Lett. 2003, 3, L155 https://doi.org/10.1142/S0219477503001221
  13. Leung, H. K. Chin. J. Phys. 1997, 35, 47
  14. Dolnik, M.; Bollt, E. M. Chaos. 1998, 80, 702
  15. Hudson, J. L.; Rossler, O. E.; Killory, H. Chem. Eng. Commun. 1986, 46, 159 https://doi.org/10.1080/00986448608911404
  16. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in FORTRAN; The Art of Scientific computing- Cambridge University Press: U.K. 1996; p 704
  17. Shinbrot, T.; Muzzio, F. J. Nature 2001, 410, 251 https://doi.org/10.1038/35065689
  18. Chen, L.; Wang, J.; Zhou, T.; Aihara, K. Bioinformatics 2005, 21, 2722 https://doi.org/10.1093/bioinformatics/bti392
  19. Wang, J.; Kadar, S.; Jung, P.; Showalter, K. Phys. Rev. Lett. 1999, 82, 855 https://doi.org/10.1103/PhysRevLett.82.855
  20. Boukal, D. S.; Krivan, V. J. Math. Biol. 1999, 39, 493 https://doi.org/10.1007/s002850050009
  21. Munuzuri, V. P.; Sagues, F.; Sancho, J. M. Phys. Rev. E 2000, 62, 94 https://doi.org/10.1103/PhysRevE.62.94
  22. Alonso, S.; Sagues, F. Phys. Rev. E 2001, 63, 46205

Cited by

  1. Physical Chemistry Research Articles Published in the Bulletin of the Korean Chemical Society: 2003-2007 vol.29, pp.2, 2008, https://doi.org/10.5012/bkcs.2008.29.2.450
  2. Nonlinear Entropy Production in a Reversible Oregonator Model vol.29, pp.5, 2006, https://doi.org/10.5012/bkcs.2008.29.5.1051