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The European Physical Journal Special Topics

, Volume 227, Issue 7–9, pp 747–756 | Cite as

Stochastic switching in systems with rare and hidden attractors

  • Nataliya Stankevich
  • Erik Mosekilde
  • Aneta Koseska
Regular Article
Part of the following topical collections:
  1. Nonlinear Effects in Life Sciences

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.

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References

  1. 1.
    P. Heyward, M. Ennis, A. Keller, M.T. Shipley, J. Neurosci. 21, 5311 (2001) CrossRefGoogle Scholar
  2. 2.
    J.R. Pomerening, E.D. Sontag, J.E. Ferrell, Nat. Cell Biol. 5, 346 (2003) CrossRefGoogle Scholar
  3. 3.
    Y. Loewenstein, S. Mahon, P. Chadderton, K. Kitamura, H. Sompolinsky, Y. Yarom, M. Häusser, Nat. Neurosci. 8, 202 (2005) CrossRefGoogle Scholar
  4. 4.
    J.A.S. Kelso, Philos. Trans. R. Soc. B 367, 906 (2012) CrossRefGoogle Scholar
  5. 5.
    A.N. Pisarchik, U. Feudel, Phys. Rep. 540, 167 (2014) ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    E. Kussell, S. Leibler, Science 309, 2075 (2005) ADSCrossRefGoogle Scholar
  7. 7.
    M. Acar, J.T. Mettetal, A. Van Oudenaarden, Nat. Genet. 40, 471 (2008) CrossRefGoogle Scholar
  8. 8.
    A. Koseska, A. Zaikin, J. García-Ojalvo, J. Kurths, Phys. Rev. E 75, 031917 (2007) ADSCrossRefGoogle Scholar
  9. 9.
    A. Koseska, A. Zaikin, J. Kurths, J. García-Ojalvo, PLoS One 4, e4872 (2009) ADSCrossRefGoogle Scholar
  10. 10.
    N. Suzuki, C. Furusawa, K. Kaneko, PloS One 6, e27232 (2011) ADSCrossRefGoogle Scholar
  11. 11.
    G. Cymbalyuk, Phys. Rev. E 84, 041910 (2011) ADSCrossRefGoogle Scholar
  12. 12.
    T. Malashchenko, A. Shilnikov, G. Cymbalyuk, PLoS One 6, e21782 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    T. Malashchenko, A. Shilnikov, G. Cymbalyuk, Phys. Rev. E 84, 041910 (2011) ADSCrossRefGoogle Scholar
  14. 14.
    W. Barnett, G. OB́rien, G. Cymbalyuk, J. Neurosci. Meth. 220, 179 (2011) CrossRefGoogle Scholar
  15. 15.
    B. Marin, W.H. Barnett, A. Doloc-Mihu, R.L. Calabrese, G. Cymbalyuk, PLoS One 9, 1002930 (2013) Google Scholar
  16. 16.
    G. Cymbalyuk, Multistability in Neurodynamics: Overview, in Encyclopedia of Computational Neuroscience, edited by D. Jaeger, R. Jung (Springer, New York, NY, 2015) Google Scholar
  17. 17.
    A. Sherman, Bull. Math. Biol. 56, 811 (1994) Google Scholar
  18. 18.
    J. Jalife, C. Antzelevitch, Science 206, 695 (1979) ADSCrossRefGoogle Scholar
  19. 19.
    A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952) CrossRefGoogle Scholar
  20. 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) Google Scholar
  21. 21.
    K. Kaneko, Phys. Rev. Lett. 78, 2736 (1997) ADSCrossRefGoogle Scholar
  22. 22.
    G.A. Leonov, N.V. Kuznetsov, Int. J. Bifurc. Chaos 23, 1330002 (2013) CrossRefGoogle Scholar
  23. 23.
    D. Dudkowski, S. Jafari, T. Kapitaniak, N.V. Kuznetsov, G.A. Leonov, A. Prasad, Phys. Rep. 637, 1 (2016) ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    A. Raj, A. van Oudenaarden, Cell 135, 216 (2008) CrossRefGoogle Scholar
  25. 25.
    D.K. Wells, W.L. Kath, A.E. Motter, Phys. Rev. X 5, 031036 (2015) Google Scholar
  26. 26.
    S. Brezetskyi, D. Dudkowski, T. Kapitaniak, Eur. Phys. J. Special Topics 224, 1459 (2015) ADSCrossRefGoogle Scholar
  27. 27.
    N.V. Stankevich, E. Mosekilde, Chaos 27, 123101 (2017) ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    A.A. Hill, J. Lu, M.A. Masino, O.H. Olsen, R.L. Calabrese, J. Comput. Neurosci. 10, 281 (2001) CrossRefGoogle Scholar
  29. 29.
    A. Zakharova, T. Vadivasova, V. Anishchenko, A. Koseska, J. Kurths, Phys. Rev. E 81, 011106 (2010) ADSCrossRefGoogle Scholar
  30. 30.
    N.K. Kamal, V. Varshney, M.D. Shrimali, A. Prasad, N.V. Kuznetsov, G.A. Leonov, Nonlinear Dyn. 91, 1 (2018) CrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Nataliya Stankevich
    • 1
    • 2
  • Erik Mosekilde
    • 3
  • Aneta Koseska
    • 4
  1. 1.Department of Applied CyberneticsSt. Petersburg State UniversitySaint-PetersburgRussia
  2. 2.Department of Radio-Electronics and TelecommunicationsYuri Gagarin State Technical University of SaratovSaratovRussia
  3. 3.Department of PhysicsThe Technical University of DenmarkLyngbyDenmark
  4. 4.Department of Systemic Cell BiologyMax Planck Institute of Molecular PhysiologyDortmundGermany

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