Abstract
Simulation results of bistable perception due to ambiguous visual stimuli are presented which are obtained with a behavioral nonlinear dynamics model using perception–attention–memory coupling. This model provides an explanation of recent experimental results of Gao et al. (Cogn Process 7:105–112, 2006a) and it supports their speculation that the fractal character of perceptual dominance time series may be understood in terms of nonlinear and reentrant dynamics of brain processing. Percept reversals are induced by attention fatigue and noise, with an attention bias which balances the relative percept duration. Dynamical coupling of the attention bias to the perception state introduces memory effects leading to significant long range correlations of perceptual duration times as quantified by the Hurst parameter H > 0.5 (Mandelbrot, The fractal geometry of nature, 1991), in agreement with Gao et al. (Cogn Process 7:105–112, 2006a).
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References
Anishchenko VS, Astakhov VV, Neiman AB, Vadivasova TE, Schimanski-Geier L (2003) Nonlinear dynamics of chaotic and stochastic systems. Springer, Berlin
Arnold DA, Grove PM, Wallis TSA (2007) Staying focused: a functional account of perceptual suppression during binocular rivalry. J Vis 7: 1–8
Atmanspacher H, Filk T, Römer H (2004) Quantum Zeno features of bistable perception. Biol Cybern 90: 33–40
Beran J (1992) Statistical methods for data with long-range dependence. Stat Sci 7: 404–427
Blake R, Logothetis NK (2002) Visual competition. Nat Rev Neurosci 3: 1–11
Born M, Wolf E (1975) Principles of optics, 5th edn. Pergamon Press, Oxford
Borsellino A, de Marco A, Allazetta A, Rinesi S, Bartolini B (1972) Reversal time distribution in the perception of visual ambiguous stimuli. Kybernetik 10: 139–144
Braskamp JE, van Ee R, Noest AJ, Jacobs RH, van den Berg AV (2006) The time course of binocular rivalry reveals a fundamental role of noise. J. Vis 6: 1244–1256
Burke DP, de Paor AM (2004) A stochastic limit cycle oscillator model of the EEG. Biol Cybern 91: 221–230
Busenberg S, Martinelli M (eds) (1991) Delay differential equations and dynamical systems. Lecture Notes in Mathematics, vol 1475. Springer, New York
Dafilis MP, Liley DTJ, Cadusch PJ (2001) Robust chaos in a model of the electroencephalogram: Implications for brain dynamics. Chaos 11: 474–478
Deco G, Marti D (2007) Deterministic analysis of stochastic bifurcations in multi-stable neurodynamical systems. Biol Cybern 96: 487–496
deGuzman GC, Kelso JAS (1991) Multifrequency behavioral patterns and the phase attractive circle map. Biol Cybern 64: 485–495
De Marco A, Penengo P, Trabucco A, Borsellino A, Carlini F, Riani M, Tuccio MT (1977) Stochastic models and fluctuations in reversal time of ambiguous figures. Perception 6: 645–656
Derstine MW, Jewell JL, Gibbs HM, Hopf FA, Rushford MC, Sanders LD, Tai K (1987) Experimental verification of regenerative pulastions and chaos. In: Arecchi FT, Harrison RG (eds) Instabilities and chaos in quantum optics. Springer Series in Synergetics, vol 34. Springer, Berlin, pp 175–198
Ditzinger T, Haken H (1989) Oscillations in the perception of ambiguous patterns. Biol Cybern 61: 279–287
Ditzinger T, Haken H (1995) A synergetic model of multistability in perception. In: Kruse P, Stadler M (eds) Ambiguity in mind and nature. Springer, Berlin, pp 255–273
Dodson CTJ, Scharcanski J (2003) Information geometric similarity measurement for near-random stochastic processes. IEEE Trans Syst Man Cybern A 33: 435–440
Edelman G (2004) Wider than the sky. Penguin Books, New York, pp 87–96
Engel AK, Fries P, König P, Brecht M, Singer W (1999) Temporal binding, binocular rivalry, and consciousness. Conscious Cogn 8: 128–151
Engel AK, Fries P, Singer W (2001) Dynamic predictions: oscillations and synchrony in top-down processing. Nat Rev Neurosci 2: 704–718
Feigenbaum MJ (1979) The universal metric properties of nonlinear transformations. J. Stat Phys 21: 669–706
Frank TD, Michelbrink M, Beckmann H, Schöllhorn WI (2008) A quantitative dynamical systems approach to differential learning: self-organization principle and orderparameter equations. Biol Cybern 98: 19–31
Freeman WJ (2000) Neurodynamics: an exploration in mesoscopic brain dynamics. Springer, Berlin
Fürstenau N (2003) Nonlinear dynamics model of cognitive multistability and binocular rivalry. Proceedings IEEE 2003 International Conference on Systems, Man and Cybernetics, IEEE cat. no. 03CH37483C, pp 1081–1088
Fürstenau N (2004) A chaotic attractor model of cognitive multistability. Proceedings IEEE 2004 International Conference on Systems, Man and Cybernetics, IEEE cat. no. 04CH37583C, pp 853–859
Fürstenau N (2006) Modelling and simulation of spontaneous perception switching with ambiguous visual stimuli in augmented vision systems. Lecture Notes in Artificial Intelligence, vol 4021. Springer, Berlin, pp 20–31
Fürstenau N (2007) A computational model of bistable perception–attention dynamics with long range correlations. In: Hertzberg J, Beetz M, Englert R (eds) KI2007, Lecture Notes in Artificial Intelligence LNAI 4667. Springer, Berlin, pp 251–263
Fürstenau N (2009) Computational nonlinear dynamics model of percept switching with ambiguous stimuli. In: Duffy VG (ed) HCII2009, Lecture Notes in Computer Science, LNCS 5620. Springer, Berlin, pp 227–236
Gao JB, Merk I, Tung WW, Billok V, White KD, Harris JG, Roychowdhury VP (2006a) Inertia and memory in visual perception. Cogn. Process 7: 105–112
Gao J, Hu J, Tung WW, Yinhe C, Sarshar N, Roychowdhury VP (2006b) Assessment of long-range correlation in time series: how to avoid pitfalls. Phys Rev E 73: 016117-1–016117-10
Gao J, Hu J, Tung WW, Cao YH (2006c) Distinguishing chaos from noise by scale dependent Lyapunov exponent. Phys Rev E 74: 066204-1–066204-9
Gao J, Cao Y, Tung W-W, Jing H (2007) Multiscale analysis of complex time series. Wiley-Interscience, Hoboken, NJ
Haken H (1978) Synergetics, 2nd edn. Springer, Berlin
Haken H (2002) Brain dynamics. Springer, Berlin
Haken H, Kelso JAS, Bunz H (1985) A theoretical model for phase transitions in human movement. Biol Cybern 53: 247–257
Hamker FH (2004) A dynamic model of how feature cues guide spatial attention. Vis Res 44: 501–521
Hillyard SA, Vogel EK, Luck SJ (1999) Sensory gain control (amplification) as a mechanism of selective attention: electrophysiological and neuroimaging evidence. Philos Trans R Soc Lond B 353(1373): 1257–1270
Hock HS, Kelso JAS, Schöner G (1993) Bistability and hysteresis in the organisation of apparent motion patterns. J Exp Psychol 19: 63–80
Hock HS, Schöner G, Voss A (1997) The influence of adaptation and stochastic fluctuations on spontaneous perceptual changes for bistable stimuli. Percep Psychophys 59: 509–522
Hock HS, Schöner G, Giese M (2003) The dynamical foundations of motion pattern formation: stability, selective adaptation, and perceptual continuity. Percep Psychophys 65: 429–457
Ikeda K, Matsumoto K (1987) High dimensional chaotic behavior in systems with time delayed feedback. Physica 29D: 223–235
Ito J, Nikolaev AR, Luman M, Aukes MF, Nakatani C, van Leeuwen C (2003) Perceptual switching, eye movements, and the bus paradox. Perception 32: 681–698
Itti L, Koch C (2001) Computational modelling of visual attention. Nat Rev Neurosci 2: 194–203
Jirsa V, Haken H (1996) Field theory of electromagnetic brain activity. Phys Rev Lett 77(5): 960–963
Jirsa V, Haken H (1997) A derivation of a macroscopic field theory of the brain from quasi microscopic neural dynamics. Physica D99: 503–526
Kelso JAS (1995) Dynamic patterns: the self-organization of brain and behavior. The MIT Press, Cambridge, London
Kelso JAS, Bressler SL, Buchanan S, DeGuzman GC, Ding M, Fuchs A, Holroyd T (1992) A phase transition in human brain and behavior. Phys Lett A 169: 134–144
Kelso JAS, Case P, Holroyd T, Horvath E, Raczaszek J, Tuller B, Ding M (1995) Multistability and metastability in perceptual and brain dynamics. In: Kruse P, Stadler M (eds) Ambiguity in mind and nature. Springer, Berlin, pp 255–273
Kettani H, Gubner JA (2006) A novel approach to the estimation of the long-range dependence parameter. IEEE Trans Circ Syst II 53: 463–467
Lamme VAF (2003) Why visual attention and awareness are different. Trends Cogn Sci 7: 12–18
Levelt WJM (1967) Note on the distribution of dominance times in binocular rivalry. Br J Psychol 58: 143–145
Lehky SR (1995) Binocular rivalry is not chaotic. Proc R Soc Lond B 259: 71–76
Loxley PN, Robinson PA (2009) Soliton model of competitive neural dynamics during binocular rivalry. Phys Rev Lett 102: 258701-1–258701-4
Lutzenberger W, Preissl H, Pulvermüller F (1995) Fractal dimension of electroencephalographic time series and underlying brain processes. Biol Cybern 73: 477–482
MacDonald N (1989) Biological delay systems: linear stability analysis. Cambridge University Press, Cambridge
Magnus K (1961) Schwingungen. Teubner, Stuttgart
Mandelbrot BB (1991) The fractal geometry of nature (German translation). Birkhäuser, Basel, pp 265–270
Meng M, Tong F (2004) Can attention selectively bias bistable perception? Differences between binocular rivalry and ambiguous figures. J. Vis 4: 539–551
Merk ILK, Schnakenberg J (2002) A stochastic model of multistable perception. Biol Cybern 86: 111–116
Murata T, Matsui N, Miyauchi S, Kakita Y, Yanagidu T (2003) Discrete stochastic process underlying perceptual rivalry. Neuroreport 14: 1347–1352
Nakatani H, van Leeuwen C (2005) Individual Differences in Perceptual Switching rates: the role of occipital alpha and frontal theta band activity. Biol Cybern 93: 343–354
Nakatani H, van Leeuwen C (2006) Transient synchrony of distant brain areas and perceptual switching in ambiguous figures. Biol Cybern 94: 445–457
Natsuki N, Nishimura H, Matsui N (2000) A neural chaos model of multistable perception. Neural Process Lett 12: 267–276
Noest AJ, van Ee R, Nijs MM, van Wezel RJA (2007) Percept-choice sequences driven by interrupted ambiguous stimuli: a low-level neural model. J Vis 7: 1–14
Orbach J, Ehrlich D, Heath HA (1963) Reversibility of the Necker cube: an examination of the concept of satiation of orientation. Percep Motor Skills 17: 439–458
Patterson R, Winterbottom M, Pierce B, Fox R (2007) Binocular rivalry and head worn displays. Hum Fact 49: 1083–1096
Pitts MA, Nerger JL, Davis TJR (2007) Electrophysiological correlates of perceptual reversals for three different types of multistable images. J Vis 7: 1–14
Poston T, Stewart I (1978) Nonlinear modeling of multistable perception. Behav Sci 23: 318–334
Richards W, Wilson HR, Sommer MA (1994) Chaos in percepts. Biol Cybern 70: 345–349
Robinson, D (eds) (1998) Neurobiology. Springer, Berlin
Robinson PA (2005) Propagator theory of brain dynamics. Phys Rev E72: 011904-1–011904-14
Schuster HG, Just W (2005) Deterministic chaos, 4th edn. Wiley-VCH, Weinheim
Schuster HG, Wagner PA (1990) A model for neural oscillations in the visual cortex: 1. Mean field theory and the derivation of the phase equations. Biol Cybern 64: 77–82
Srinavasan R, Russel DS, Edelman GM, Tononi G (1999) Increased synchronization of magnetic responses during conscious perception. J Neurosci 19: 5435–5448
Tononi G, Edelman GM (1998) Consciousness and complexity. Science 282: 1846–1851
von der Malsburg C (1997) The coherence definition of consciousness. In: Ho M, Miyashita Y, Rolls ET (eds) Cognition, computation, and consciousnesss. Oxford University Press, v, pp 193–204
Watts C, Fürstenau N (1989) Multistable fiber-optic Michelson Interferometer exhibiting 95 stable states. IEEE J Quantum Electron 25: 1–5
Wilson HR (1999) Spikes, decisions, and actions. Oxford University Press, Oxford
Zhou YH, Gao JB, White KD, Merk I, Yao K (2004) Perceptual dominance time distributions in multistable visual perception. Biol Cybern 90: 256–263
Acknowledgments
I am indebted to Monika Mittendorf for help with the computer experiments and data evaluation, to H. Nakatani of Riken Brain Science Institute for information on recent experimental results, and, in particular, to J.B. Gao and K.D. White of University of Florida for providing an early preprint of their study. J. B. G. is now with PMB Intelligence LLC. Significant improvements of the original version of the manuscript are due to valuable comments and questions of the anonymous reviewers.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Fürstenau, N. A nonlinear dynamics model for simulating long range correlations of cognitive bistability. Biol Cybern 103, 175–198 (2010). https://doi.org/10.1007/s00422-010-0388-4
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DOI: https://doi.org/10.1007/s00422-010-0388-4