Bistable perception of ambiguous images: simple Arrhenius model

  • E. Z. MeilikhovEmail author
  • R. M. Farzetdinova
Research Article


Watching an ambiguous image leads to the bistability of its perception, that randomly oscillates between two possible interpretations. The relevant evolution of the neuron system is usually described with the equation of its “movement” over the nonuniform energy landscape under the action of the stochastic force, corresponding to noise perturbations. We utilize the alternative (and simpler) approach suggesting that the system is in the quasi-stationary state being described by the Arrhenius equation. The latter, in fact, determines the probability of the dynamical variation of the image being percepted (for example, the left Necker cube \(\leftrightarrow\) the right Necker cube) along one scenario or another. Probabilities of transitions from one perception to another are defined by barriers detaching corresponding wells of the energy landscape, and the relative value of the noise (analog of temperature) influencing this process. The mean noise value could be estimated from experimental data. The model predicts logarithmic dependence of the perception hysteresis width on the period of cyclic sweeping the parameter, controlling the perception (for instance, the contrast of the presented object). It agrees with the experiment and allows to estimate the time interval between two various perceptions.


Ambiguous images Analytic theory Bistable perception Perception hysteresis 



  1. Burns BD (1968) The Uncertain Nervous System. Edward Arnold (Publishers) Ltd., LondonGoogle Scholar
  2. Haken H (1996) Principles of brain functioning. Springer, BerlinCrossRefGoogle Scholar
  3. Huguet G, Rinzel J, Hupé J-M (2014) Noise and adaptation in multistable perception: noise drives when to switch, adaptation determines percept choice. J Vis 14(3):19CrossRefGoogle Scholar
  4. Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284–304CrossRefGoogle Scholar
  5. Lago-Fernández LF, Deco G (2002) A model of binocular rivalry based on competition in IT. Neurocomputing 44:503–507CrossRefGoogle Scholar
  6. Laing CR, Chow CC (2002) A spiking neuron model for binocular rivalry. J Comput Neurosci 12:39–53CrossRefGoogle Scholar
  7. Lehky SR (1995) An astable multivibrator model of binocular rivalry. Perception 17(215–228):1988Google Scholar
  8. Leopold DA, Logothetis NK (1999) Multistable phenomena: changing views in perception. Trends Cognit Sci (Regul. Ed.) 3:254–264CrossRefGoogle Scholar
  9. Levelt WJM (1968) On binocular rivalry. Mouton, ParisGoogle Scholar
  10. Long GM, Toppino TC (2004) Enduring interest in perceptual ambiguity: alternating views of reversible figures. Psychol Bull 130:748–768CrossRefGoogle Scholar
  11. Merk I, Schnakenberg J (2002) A stochastic model of multistable visual perception. Biol Cybern 86:111–116CrossRefGoogle Scholar
  12. Moreno-Bote R, Rinzel J, Rubin N (2007) Noise-induced alternations in an attractor network model of perceptual bistability. J Neurophys 98:1125–1139CrossRefGoogle Scholar
  13. Necker L (1832) Observations on some remarkable phenomenon which occurs on viewing a figure of a crystal of geometrical solid. Lond Edinb Philos Mag J Sci 3:329–337Google Scholar
  14. Pisarchik AN, Jaimes-Reátegui R, Alejandro Magallón-Garcia CD, Obed C-MC (2014) Critical slowing down and noise-induced intermittency in bistable perception: bifurcation analysis. Cybern Biol. Google Scholar
  15. Poston T, Stewart I (1978) Catastrophe theory and its applications. Pitman, New YorkGoogle Scholar
  16. Pressnitzer D, Hupé JM (2006) Temporal dynamics of auditory and visual bistability reveal common principles of perceptual organization. Curr Biol 16:1351–1357CrossRefGoogle Scholar
  17. Runnova AE, Hramov AE, Grubov VV, Koronovskii AE, Kurovskaya MK, Pisarchik AN (2016) Chaos. Solitons Fractals 93:201–206CrossRefGoogle Scholar
  18. Sterzer P, Kleinschmidt A, Rees G (2009) The neural bases of multistable perception. Trends Cognit Sci 13(7):310–318CrossRefGoogle Scholar
  19. Stiller W (1989) Arrhenius equation and non-equlibrium kinetics. BSB B.G. Teubner Verlagsgesellschaft, LeipzigGoogle Scholar
  20. Toledano J-C, Toledano P (1987) The Landau theory of phase transitions. World Scientific, SingaporeCrossRefGoogle Scholar
  21. Urakawa T, Bunya M, Araki O (2017) Involvement of the visual change detection process in facilitating perceptual alternation in the bistable image. Cogn Neurodyn 11(4):307–318CrossRefGoogle Scholar
  22. Vonsovsky SV (1974) Magnetism. Wiley, LondonGoogle Scholar
  23. Wilson HR, Blake R, Lee SH (2001) Dynamics of travelling waves in visual perception. Nature 412(6850):907–910CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Nat. Res. Centre “Kurchatov Institute”MoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia

Personalised recommendations