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Critical slowing down and noise-induced intermittency in bistable perception: bifurcation analysis

Abstract

Stochastic dynamics and critical slowing down were studied experimentally and numerically near the onset of dynamical bistability in visual perception under the influence of noise. Exploring the Necker cube as the essential example of an ambiguous figure, and using its wire contrast as a control parameter, we measured dynamical hysteresis in two coexisting percepts as a function of both the velocity of the parameter change and the background luminance. The bifurcation analysis allowed us to estimate the level of cognitive noise inherent to brain neural cells activity, which induced intermittent switches between different perception states. The results of numerical simulations with a simple energy model are in good qualitative agreement with psychological experiments.

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References

  • Aks DJ, Sprott JC (2003) The role of depth and 1/f dynamics in perceiving reversible figures. Nonlinear Dyn Psychol Life Sci 7(2):161–180

    Article  Google Scholar 

  • Atteneave F (1971) Multistability in perception. Sci Am 225:63–71

    Article  Google Scholar 

  • Borisyuk R, Chik D, Kazanovich Y (2009) Visual perception of ambiguous figures: synchronization based neural models. Biol Cybern 100:491–504

    PubMed  Article  Google Scholar 

  • Broggi G, Colombo A, Lugiato LA, Mandel P (1986) Influence of white noise on delayed bifurcations. Phys Rev A 33:3635–3636

    CAS  PubMed  Article  Google Scholar 

  • Chialvo DR, Apkarian AV (1993) Modulated noisy biological dynamics: three examples. J Stat Phys 70(1/2):375–391

    Article  Google Scholar 

  • Deco G, Rolls ET, Romo R (2009) Stochastic dynamics as a principle of brain function. Prog Neurobiol 88:1–16

    PubMed  Article  Google Scholar 

  • Figley CR, Sprenkle DH (1978) Delayed stress response syndrome: family therapy indications. J Marital Fam Ther 4:5360

    Article  Google Scholar 

  • Gigante G, Mattia M, Braun J, Del Giudice P (2009) Bistable perception modeled as competing stochastic integrations at two levels. PLoS Comput Biol 5:e1000430

    PubMed Central  PubMed  Article  Google Scholar 

  • Haken H (1983) Synergetics. An Introduction. Springer, Berlin

    Google Scholar 

  • Hanson RF, Spratt EG (2000) Reactive attachment disorder: what we know about the disorder and implications for treatment. Child Maltreat 5:137–145

    CAS  PubMed  Google Scholar 

  • Hebb DO (1949) The organization of behavior. Wiley, New York

    Google Scholar 

  • Huerta-Cuellar G, Pisarchik AN, Kir’yanov AV, Barmenkov YuO, del Valle Hernández J (2009) Prebifurcation noise amplification in a fiber laser. Phys Rev E 79:036204

    CAS  Google Scholar 

  • Kalarickal GJ, Marshall JA (2000) Neural model of temporal and stochastic properties of binocular rivalry. Neurocomputing 32–33:843–853

    Google Scholar 

  • Kanai R, Moradi F, Shimojo S, Verstraten FAJ (2005) Perceptual alternation induced by visual transients. Perception 34:803–822

    PubMed  Google Scholar 

  • Kapral R, Mandel P (1985) Bifurcation structure of the non-autonomous quadratic map. Phys Rev A 32:1076–1081

    PubMed  Google Scholar 

  • Köhler W, Wallach H (1944) Figural after-effects, an investigation of visual processes. Proc Am Philos Soc 88:269–357

    Google Scholar 

  • Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284–360

    CAS  Google Scholar 

  • Lago-Fernandez LF, Deco G (2002) A model of binocular rivalry based on competition in IT. Neurocomputing 44:503–507

    Google Scholar 

  • Leopold DA, Wilke M, Maier A, Logothetis NK (2002) Stable perception of visually ambiguous patterns. Nat Neurosci 5:605609

    Google Scholar 

  • Mandel P, Erneux T (1984) Laser Lorenz equations with a time-dependent parameter. Phys Rev Lett 53:1818–1820

    CAS  Google Scholar 

  • Merk I, Schnakenberg J (2002) A stochastic model of multistable visual perception. Biol Cybern 86:111–116

    CAS  PubMed  Google Scholar 

  • Meyn SP, Tweedie RL (eds) (2008) Markov Chains and stochastic stability. Cambridge University Press, Cambridge

  • Moreno-Bote R, Rinzel J, Rubin N (2007) Noise-induced alternations in an attractor network model of perceptual bistability. J Neurophysiol 98:11251139

    Google Scholar 

  • Moreno-Bote R, Knill DC, Pouget A (2011) Bayesian sampling in visual perception. PNAS. doi:10.1073/pnas.1101430108

  • Pisarchik AN, Feudel U (2014) Control of multistability. Physics Reports (in press). doi:10.1016/j.bbr.2011.03.031

  • Pisarchik AN, Chizhevsky VN, Corbalán R, Vilaseca R (1997) Experimental control of nonlinear dynamics by slow parametric modulation. Phys Rev E 55(3):2455–2461

    CAS  Google Scholar 

  • Pisarchik AN (1998) Dynamical tracking of periodic orbits. Phys Lett A 242(3):152–162

    CAS  Google Scholar 

  • Pisarchik AN, Pochepen ON, Pisarchyk LA (2012) Increasing blood glucose variability is a precursor of sepsis and mortality in burned patients. PLoS One 7(10):e46582

    CAS  PubMed Central  PubMed  Google Scholar 

  • Rolls ET (2008) Emotion, higher order syntactic thoughts, and consciousness. In: Weiskrantz I, Davies MK (eds) Frontiers of consciousness. Oxford University Press, Oxford, pp 131–167

    Google Scholar 

  • Rolls ET (2008) Memory, attention, and decision-making: a unifying computational neuroscience approach. Oxford University Press, Oxford

    Google Scholar 

  • Schwartz J-L, Grimault N, Hupé J-M, Moore CJBCJ, Pressnitzer D (2012) Multistability in perception: sensory modalities, an overview. Phil Trans R Soc B 367:896–905

    PubMed Central  PubMed  Google Scholar 

  • Shpiro A, Moreno-Bote R, Rubin N, Rinzel J (2009) Balance between noise and adaptation in competition models of perceptual bistability. J Comput Neurosci. doi:10.1007/s10827-008-0125-3

  • Simonotto E, Riani M, Seife C, Roberts M, Twitty J, Moss F (1997) Visual perception of stochastic resonance. Phys Rev Lett 78(6):1186–1189

    CAS  Google Scholar 

  • Ta’edd LK, Ta’eed O, Wright JE (1988) Determinants involved in the perception of the necker cube: an application of catastrophe theory. Behav Sci 33(2):97–115

    Google Scholar 

  • Tolhurst DJ, Movshon JA, Dean AF (1983) The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vis Res 23:775–785

    CAS  PubMed  Google Scholar 

  • Tredicce JR, Lippi GL, Mandel P, Charasse B, Chevalier A, Picqué B (2004) Critical slowing down at a bifurcation. Am J Phys 72:799–809

    Google Scholar 

  • World Medical Association (2000) Declaration of Helsinki: ethical principles for medical research involving human subjects. JAMA 284(23):3043–3045

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Acknowledgments

We thank K. M. Prado-Tabares for her help in the data collection and all voluntaries for their participation in the experiments. A. N. P. acknowledges support from CONACYT (Mexico).

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Correspondence to Alexander N. Pisarchik.

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This work has been supported by the COECYTJAL-UdeG through project 05-2010-1-783.

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Pisarchik, A.N., Jaimes-Reátegui, R., Magallón-García, C.D.A. et al. Critical slowing down and noise-induced intermittency in bistable perception: bifurcation analysis. Biol Cybern 108, 397–404 (2014). https://doi.org/10.1007/s00422-014-0607-5

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  • DOI: https://doi.org/10.1007/s00422-014-0607-5

Keywords

  • Perception
  • Bifurcation
  • Noise
  • Brain
  • Dynamics