Skip to main content
SpringerLink
Log in

Distributions of first passage times in a bistable thermochemical system with a low temperature stationary state

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

Abstract

We consider the influence of internal fluctuations on the behavior of a bistable thermochemical system with a low temperature stable focus surrounded by a stable limit cycle arising from the subcritical Hopf bifurcation. We use a master equation approach to study the transitions between basins of these attractors. Distribution functions of first passage times from the limit cycle to the focus are obtained for systems with various numbers of molecules and reaction heats. We consider in detail the specific, multi-peak form of the distributions caused by eccentric location of the limit cycles with respect to the focus.

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. Ch. Modchang, S. Nadkarni, T.M. Bartol, W. Triampo, T.J. Sejnowski, H. Levine, W.J. Rappel, Phys. Biol. 7, 026008 (2010)

    Article  ADS  Google Scholar 

  2. R.C. Hilborn, B. Brookshire, J. Mattingly, A. Purushotham, A. Sharma, PLoS One 7, e34536 (2012)

    Article  ADS  Google Scholar 

  3. G. Nicolis, I. Prigogine, Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977)

  4. N.G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland Pub., Amsterdam, 1987)

  5. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)

    Article  ADS  Google Scholar 

  6. A. Lemarchand, B. Nowakowski, J. Phys.: Condens. Matter 19, 065130 (2007)

    Article  ADS  Google Scholar 

  7. A. Hutt, Europhys. Lett. 84, 34003 (2008)

    Article  ADS  Google Scholar 

  8. H. Qian, Nonlinearity 24, R19 (2011)

    Article  ADS  MATH  Google Scholar 

  9. B. Lindner, J. Garcia-Ojalvo, A. Neiman, L. Schimansky-Geier, Phys. Rep. 392, 321 (2004)

    Article  ADS  Google Scholar 

  10. C.S. Zhou, J. Kurths, E. Allaria, S. Boccaletti, R. Meucci, F.T. Arecchi, Phys. Rev. E 67, 066220 (2003)

    Article  ADS  Google Scholar 

  11. M.K. Sen, A. Baura, B.Ch. Bag, J. Stat. Mech. 2009, P11004 (2009)

    Article  Google Scholar 

  12. P. Hänggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1990)

    Article  ADS  Google Scholar 

  13. B. Nowakowski, A.L. Kawczyński, ChemPhysChem. 7, 502 (2006)

    Article  Google Scholar 

  14. A.L. Kawczynski, B. Nowakowski, Phys. Chem. Chem. Phys. 10, 289 (2008)

    Article  Google Scholar 

  15. A.L. Kawczyński, B. Nowakowski, Phys. Rev. E 68, 036218 (2003)

    Article  ADS  Google Scholar 

  16. Y. Hasegawa, M. Arita, Phys. Lett. A 375 (39), 3450 (2011)

    Article  ADS  MATH  Google Scholar 

  17. T. Verechtchaguina, I.M. Sokolov, L. Schimansky-Geier, Phys. Rev. E 73, 031108 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  18. A. Kolbus, A. Lemarchand, A.L. Kawczyński, B. Nowakowski, Phys. Chem. Chem. Phys. 12, 13224 (2010)

    Article  Google Scholar 

  19. B. Nowakowski, A.L. Kawczyński, A. Kolbus, A. Lemarchand, Eur. Phys. J. B 84, 137 (2011)

    Article  ADS  Google Scholar 

  20. D.T. Gillespie, J. Comput. Phys. 22, 403 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  21. D.T. Gillespie, J. Phys. Chem. 81, 2340 (1997)

    Article  Google Scholar 

  22. F. Baras, M. Malek Mansour, Adv. Chem. Phys. 100, 393 (1997)

    Article  Google Scholar 

  23. B. Nowakowski, A. Lemarchand, Phys. Rev. E 64, 061108 (2001)

    Article  ADS  Google Scholar 

  24. B. Nowakowski, A. Lemarchand, Physica A 311, 80 (2002)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Chemistry, Jan Kochanowski University, Swiȩtokrzyska 15G, 25-406, Kielce, Poland

    Anna Kolbus

  2. Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224, Warsaw, Poland

    Bogdan Nowakowski & Andrzej L. Kawczyński

  3. Physics Laboratory, Warsaw University of Life Sciences – SGGW, Nowoursynowska 159, 02-776, Warsaw, Poland

    Bogdan Nowakowski

Authors
  1. Anna Kolbus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bogdan Nowakowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrzej L. Kawczyński
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anna Kolbus.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kolbus, A., Nowakowski, B. & Kawczyński, A. Distributions of first passage times in a bistable thermochemical system with a low temperature stationary state. Eur. Phys. J. B 86, 262 (2013). https://doi.org/10.1140/epjb/e2013-31146-9

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2013-31146-9

Keywords

Search

Navigation