Indian Journal of Physics

, Volume 91, Issue 1, pp 57–62 | Cite as

Stochastic sensitivity of a bistable energy model for visual perception

  • Alexander N. Pisarchik
  • Irina Bashkirtseva
  • Lev Ryashko
Original Article


Modern trends in physiology, psychology and cognitive neuroscience suggest that noise is an essential component of brain functionality and self-organization. With adequate noise the brain as a complex dynamical system can easily access different ordered states and improve signal detection for decision-making by preventing deadlocks. Using a stochastic sensitivity function approach, we analyze how sensitive equilibrium points are to Gaussian noise in a bistable energy model often used for qualitative description of visual perception. The probability distribution of noise-induced transitions between two coexisting percepts is calculated at different noise intensity and system stability. Stochastic squeezing of the hysteresis range and its transition from positive (bistable regime) to negative (intermittency regime) are demonstrated as the noise intensity increases. The hysteresis is more sensitive to noise in the system with higher stability.


Visual perception Bistable model Noise Hysteresis 


05.45.-a 05.40.Ca 87.10.Ed 87.10.Mn 87.18.Tt 



L. R. and I. B. acknowledge support from the Russian Science Foundation (No. 16-11-10098).


  1. [1]
    D J Tolhurst, J A Movshon and A F Dean Vis. Res. 23 775 (1983)CrossRefGoogle Scholar
  2. [2]
    A S Pikovsky and J Kurths Phys. Rev. Lett. 78 775 (1997)ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    M D McDonnel, l N G Stocks, C E M Pearce and D Abbott Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization (Cambridge : Cambridge University Press) (2008)CrossRefMATHGoogle Scholar
  4. [4]
    F Gassmann Phys. Rev. E 55 2215 (1997)ADSCrossRefGoogle Scholar
  5. [5]
    L Arnold Random Dynamical Systems (Berlin: Springer) (1998)Google Scholar
  6. [6]
    N Kogo, A Galli and J Wagemans Vis. Res. 51 2085 (2011)Google Scholar
  7. [7]
    L A Necker The London and Edinburgh Philosophical Magazine and Journal of Science 1 (5) 329 (1832)Google Scholar
  8. [8]
    E Rubin Visuell Wahrgenommene Figuren (Copenhagen: Glydenalske Boghande) (1921)Google Scholar
  9. [9]
    S Kraut, U Feudel and C Grebogi Phys. Rev. E 59 5253 (1999)ADSCrossRefGoogle Scholar
  10. [10]
    L Zhang, A Song and J He J. Phys. A: Math. Theor. 42 475003 (2009)ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    J Li and L Zeng J. Phys. A: Math. Theor. 43 495002 (2010)ADSCrossRefGoogle Scholar
  12. [12]
    A N Pisarchik and U Feudel Phys. Rep. 540 167 (2014)ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    I A Bashkitseva and L Ryashko Chaos Solitons and Fractals 26 1437 (2005)ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    I Bashkirtseva, G Chen and L Ryashko Chaos 22 033104 (2012)ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    I Merk and J Schnakenberg Biol. Cybern. 86 111 (2002)CrossRefGoogle Scholar
  16. [16]
    L K Taédd, O Taéed and J E Wright Behav. Sci. 33 97 (1988)CrossRefGoogle Scholar
  17. [17]
    D J Aks and J C Sprott Nonlinear Dyn. Psychol. Life Sci. 7 161 (2003)CrossRefGoogle Scholar
  18. [18]
    R Moreno-Bote, R Rinzel and N Rubin J. Neurophysiol. 98 11251139 (2007)CrossRefGoogle Scholar
  19. [19]
    G Huguet, J Rinzel and J M Hupé Journal of Vision 14 19 (2014)CrossRefGoogle Scholar
  20. [20]
    I Bashkirtseva and L Ryashko Chaos 21 047514 (2011)ADSCrossRefGoogle Scholar
  21. [21]
    A N Pisarchik, R Jaimes-Reátegui, C D A Magallón-García and C O Castillo-Morales Biol. Cybern. 108 397 (2014)CrossRefGoogle Scholar

Copyright information

© Indian Association for the Cultivation of Science 2016

Authors and Affiliations

  • Alexander N. Pisarchik
    • 1
    • 2
  • Irina Bashkirtseva
    • 3
  • Lev Ryashko
    • 3
  1. 1.Center for Biomedical TechnologyTechnical University of MadridMadridSpain
  2. 2.Centro de Investigaciones en OpticaLeónMexico
  3. 3.Institute of Mathematics and Computer SciencesUral Federal UniversityYekaterinburgRussia

Personalised recommendations