Skip to main content

Stochastic switching in systems with rare and hidden attractors

The European Physical Journal Special Topics volume 227, pages 747–756 (2018)Cite this article

Abstract

Complex biochemical networks are commonly characterised by the coexistence of multiple stable attractors. This endows living systems with plasticity in responses under changing external conditions, thereby enhancing their probability for survival. However, the type of such attractors as well as their positioning can hinder the likelihood to randomly visit these areas in phase space, thereby effectively decreasing the level of multistability in the system. Using a model based on the Hodgkin–Huxley formalism with bistability between a silent state, which is a rare attractor, and oscillatory bursting attractor, we demonstrate that the noise-induced switching between these two stable attractors depends on the structure of the phase space and the disposition of the coexisting attractors to each other.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

References

  1. P. Heyward, M. Ennis, A. Keller, M.T. Shipley, J. Neurosci. 21, 5311 (2001)

    Article  Google Scholar 

  2. J.R. Pomerening, E.D. Sontag, J.E. Ferrell, Nat. Cell Biol. 5, 346 (2003)

    Article  Google Scholar 

  3. Y. Loewenstein, S. Mahon, P. Chadderton, K. Kitamura, H. Sompolinsky, Y. Yarom, M. Häusser, Nat. Neurosci. 8, 202 (2005)

    Article  Google Scholar 

  4. J.A.S. Kelso, Philos. Trans. R. Soc. B 367, 906 (2012)

    Article  Google Scholar 

  5. A.N. Pisarchik, U. Feudel, Phys. Rep. 540, 167 (2014)

    ADS  MathSciNet  Article  Google Scholar 

  6. E. Kussell, S. Leibler, Science 309, 2075 (2005)

    ADS  Article  Google Scholar 

  7. M. Acar, J.T. Mettetal, A. Van Oudenaarden, Nat. Genet. 40, 471 (2008)

    Article  Google Scholar 

  8. A. Koseska, A. Zaikin, J. García-Ojalvo, J. Kurths, Phys. Rev. E 75, 031917 (2007)

    ADS  Article  Google Scholar 

  9. A. Koseska, A. Zaikin, J. Kurths, J. García-Ojalvo, PLoS One 4, e4872 (2009)

    ADS  Article  Google Scholar 

  10. N. Suzuki, C. Furusawa, K. Kaneko, PloS One 6, e27232 (2011)

    ADS  Article  Google Scholar 

  11. G. Cymbalyuk, Phys. Rev. E 84, 041910 (2011)

    ADS  Article  Google Scholar 

  12. T. Malashchenko, A. Shilnikov, G. Cymbalyuk, PLoS One 6, e21782 (2011)

    ADS  Article  Google Scholar 

  13. T. Malashchenko, A. Shilnikov, G. Cymbalyuk, Phys. Rev. E 84, 041910 (2011)

    ADS  Article  Google Scholar 

  14. W. Barnett, G. OB́rien, G. Cymbalyuk, J. Neurosci. Meth. 220, 179 (2011)

    Article  Google Scholar 

  15. B. Marin, W.H. Barnett, A. Doloc-Mihu, R.L. Calabrese, G. Cymbalyuk, PLoS One 9, 1002930 (2013)

    Google Scholar 

  16. G. Cymbalyuk, Multistability in Neurodynamics: Overview, in Encyclopedia of Computational Neuroscience, edited by D. Jaeger, R. Jung (Springer, New York, NY, 2015)

  17. A. Sherman, Bull. Math. Biol. 56, 811 (1994)

    Google Scholar 

  18. J. Jalife, C. Antzelevitch, Science 206, 695 (1979)

    ADS  Article  Google Scholar 

  19. A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952)

    Article  Google Scholar 

  20. F. Moss, P.V.E. McClintock (eds.), Noise in Nonlinear Dynamical Systems: Theory of Noise Induced Processes in Special Applications (Cambridge University Press, New York, 1989)

  21. K. Kaneko, Phys. Rev. Lett. 78, 2736 (1997)

    ADS  Article  Google Scholar 

  22. G.A. Leonov, N.V. Kuznetsov, Int. J. Bifurc. Chaos 23, 1330002 (2013)

    Article  Google Scholar 

  23. D. Dudkowski, S. Jafari, T. Kapitaniak, N.V. Kuznetsov, G.A. Leonov, A. Prasad, Phys. Rep. 637, 1 (2016)

    ADS  MathSciNet  Article  Google Scholar 

  24. A. Raj, A. van Oudenaarden, Cell 135, 216 (2008)

    Article  Google Scholar 

  25. D.K. Wells, W.L. Kath, A.E. Motter, Phys. Rev. X 5, 031036 (2015)

    Google Scholar 

  26. S. Brezetskyi, D. Dudkowski, T. Kapitaniak, Eur. Phys. J. Special Topics 224, 1459 (2015)

    ADS  Article  Google Scholar 

  27. N.V. Stankevich, E. Mosekilde, Chaos 27, 123101 (2017)

    ADS  MathSciNet  Article  Google Scholar 

  28. A.A. Hill, J. Lu, M.A. Masino, O.H. Olsen, R.L. Calabrese, J. Comput. Neurosci. 10, 281 (2001)

    Article  Google Scholar 

  29. A. Zakharova, T. Vadivasova, V. Anishchenko, A. Koseska, J. Kurths, Phys. Rev. E 81, 011106 (2010)

    ADS  Article  Google Scholar 

  30. N.K. Kamal, V. Varshney, M.D. Shrimali, A. Prasad, N.V. Kuznetsov, G.A. Leonov, Nonlinear Dyn. 91, 1 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Cybernetics, St. Petersburg State University, Saint-Petersburg, Russia

    Nataliya Stankevich

  2. Department of Radio-Electronics and Telecommunications, Yuri Gagarin State Technical University of Saratov, Saratov, Russia

    Nataliya Stankevich

  3. Department of Physics, The Technical University of Denmark, Lyngby, Denmark

    Erik Mosekilde

  4. Department of Systemic Cell Biology, Max Planck Institute of Molecular Physiology, Dortmund, Germany

    Aneta Koseska

Authors
  1. Nataliya Stankevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik Mosekilde
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aneta Koseska
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nataliya Stankevich.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Stankevich, N., Mosekilde, E. & Koseska, A. Stochastic switching in systems with rare and hidden attractors. Eur. Phys. J. Spec. Top. 227, 747–756 (2018). https://doi.org/10.1140/epjst/e2018-800012-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2018-800012-7