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Bistable perception of ambiguous images: simple Arrhenius model

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Abstract

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.

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Notes

  1. The function of Eq. (1)-type is known in the theory of magnetics, where the first term describes the energy of magnetic anisotropy, and the second one—the energy of the magnetic moment in magnetic field [so called—Zeeman energy (Vonsovsky 1974)].

  2. In the statistical physics and electronics, the concept of the effective temperature \(T_\mathrm{eff}\) (or noise temperature) is often introduced that is one way of expressing the level of available noise power (see, for example, https://en.wikipedia.org/wiki/Noise_temperature). On the order of value, that temperature is the average fluctuation \(\langle |\Phi |\rangle\) of the relevant quantity, expressed in energy units: \(k_BT_\mathrm{eff} =\langle |\Phi |\rangle\), where \(k_B\) is the Boltzmann constant. In the text, by fluctuations we mean the deviation of ion or neurotransmitter concentrations in synaptic contacts. That is why we call this noise (and that temperature) as chemical or neural ones. This term is purely phenomenal, different processes could group together under this same heading. But, nevertheless, the electric potential of a membrane fluctuates in random manner (see Burns 1968).

  3. In the presence of noises, another phenomenon could be observed—the random intermittence that is the simultaneous switching from one image perception to another one under the constant control parameter.

  4. Parameters \(\langle \Phi \rangle /U_0,\, \gamma ,\, \tau _0\) are individual ones and, in principle, could vary in broad limits.

  5. In electrical engineering, it is known as the telegraph noise.

  6. For convenience, in the present section we use the terminology relating to the bistable perception of the Necker cube, but conclusions are applicable to any bistable system.

  7. Derivation of the obtained formulae and its form are identical to those being known for the distribution of gas particles over free path lengths.

  8. The distribution obtained is known from the theory of two-stage radioactive decay.

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Authors and Affiliations

  1. Nat. Res. Centre “Kurchatov Institute”, Moscow, Russia, 123182

    E. Z. Meilikhov & R. M. Farzetdinova

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Russia, 141707

    E. Z. Meilikhov

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  1. E. Z. Meilikhov
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  2. R. M. Farzetdinova
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Correspondence to E. Z. Meilikhov.

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Meilikhov, E.Z., Farzetdinova, R.M. Bistable perception of ambiguous images: simple Arrhenius model. Cogn Neurodyn 13, 613–621 (2019). https://doi.org/10.1007/s11571-019-09554-9

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