Skip to main content
SpringerLink
Log in

Effects of Time-Dependent Stimuli in a Competitive Neural Network Model of Perceptual Rivalry

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

We analyze a competitive neural network model of perceptual rivalry that receives time-varying inputs. Time-dependence of inputs can be discrete or smooth. Spike frequency adaptation provides negative feedback that generates network oscillations when inputs are constant in time. Oscillations that resemble perceptual rivalry involve only one population being “ON” at a time, which represents the dominance of a single percept at a time. As shown in Laing and Chow (J. Comput. Neurosci. 12(1):39–53, 2002), for sufficiently high contrast, one can derive relationships between dominance times and contrast that agree with Levelt’s propositions (Levelt in On binocular rivalry, 1965). Time-dependent stimuli give rise to novel network oscillations where both, one, or neither populations are “ON” at any given time. When a single population receives an interrupted stimulus, the fundamental mode of behavior we find is phase-locking, where the temporally driven population locks its state to the stimulus. Other behaviors are analyzed as bifurcations from this forced oscillation, using fast/slow analysis that exploits the slow timescale of adaptation. When both populations receive time-varying input, we find mixtures of fusion and sole population dominance, and we partition parameter space into particular oscillation types. Finally, when a single population’s input contrast is smoothly varied in time, 1:n mode-locked states arise through period-adding bifurcations beyond phase-locking. Our results provide several testable predictions for future psychophysical experiments on perceptual rivalry.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  • Abbott, L. F., Varela, J. A., Sen, K., & Nelson, S. B. (1997). Synaptic depression and cortical gain control. Science, 275(5297), 220–224.

    Article  Google Scholar 

  • Amari, S.-I. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern., 27(2), 77–87.

    Article  MathSciNet  MATH  Google Scholar 

  • Benda, J., & Herz, A. V. M. (2003). A universal model for spike-frequency adaptation. Neural Comput., 15(11), 2523–2564.

    Article  MATH  Google Scholar 

  • Blake, R. (1989). A neural theory of binocular rivalry. Psychol. Rev., 96(1), 145–167.

    Article  Google Scholar 

  • Blake, R., & Logothetis, N. (2002). Visual competition. Nat. Rev., Neurosci., 3, 1–11.

    Article  Google Scholar 

  • Blake, R., Sobel, K. V., & Gilroy, L. A. (2003). Visual motion retards alternations between conflicting perceptual interpretations. Neuron, 39(5), 869–878.

    Article  Google Scholar 

  • Bossink, C. J., Stalmeier, P. F., & De Weert, C. M. (1993). A test of Levelt’s second proposition for binocular rivalry. Vis. Res., 33(10), 1413–1419.

    Article  Google Scholar 

  • Brascamp, J. W., van Ee, R., Noest, A. J., Jacobs, R. H. A. H., & van den Berg, A. V. (2006). The time course of binocular rivalry reveals a fundamental role of noise. J. Vis., 6(11), 1244–1256.

    Article  Google Scholar 

  • Brascamp, J. W., Knapen, T. H. J., Kanai, R., Noest, A. J., van Ee, R., & van den Berg, A. V. (2008). Multi-timescale perceptual history resolves visual ambiguity. PLoS ONE, 3(1), e1497.

    Article  Google Scholar 

  • Brascamp, J. W., Pearson, J., Blake, R., & van den Berg, A. V. (2009). Intermittent ambiguous stimuli: implicit memory causes periodic perceptual alternations. J. Vis., 9(3), 3.1.

    Article  Google Scholar 

  • Buckthought, A., Kim, J., & Wilson, H. R. (2008). Hysteresis effects in stereopsis and binocular rivalry. Vis. Res., 48(6), 819–830.

    Article  Google Scholar 

  • Chen, X., & He, S. (2004). Local factors determine the stabilization of monocular ambiguous and binocular rivalry stimuli. Curr. Biol., 14(11), 1013–1017.

    Article  Google Scholar 

  • Coombes, S., & Bressloff, P. C. (1999). Mode locking and Arnold tongues in integrate-and-fire neural oscillators. Phys. Rev. E, 60(2 Pt B), 2086–2096.

    Article  MathSciNet  Google Scholar 

  • Curtu, R. (2010). Singular Hopf bifurcations and mixed-mode oscillations in a two-cell inhibitory neural network. Physica D, 239(9), 504–514.

    Article  MathSciNet  MATH  Google Scholar 

  • Curtu, R., Shpiro, A., Rubin, N., & Rinzel, J. (2008). Mechanisms for frequency control in neuronal competition models. SIAM J. Appl. Dyn. Syst., 7(2), 609–649.

    Article  MathSciNet  MATH  Google Scholar 

  • Fender, D., & Julesz, B. (1967). Extension of Panum’s fusional area in binocularly stabilized vision. J. Opt. Soc. Am., 57(6), 819–830.

    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(7), e1000430.

    Article  Google Scholar 

  • Harrad, R. A., McKee, S. P., Blake, R., & Yang, Y. (1994). Binocular rivalry disrupts stereopsis. Perception, 23(1), 15–28.

    Article  Google Scholar 

  • Kang, M. S., Heeger, D., & Blake, R. (2009). Periodic perturbations producing phase-locked fluctuations in visual perception. J. Vis., 9(2), 8.1.

    Article  Google Scholar 

  • Kilpatrick, Z. P., & Bressloff, P. C. (2010). Binocular rivalry in a competitive neural network with synaptic depression. SIAM J. Appl. Dyn. Syst., 9(4), 1303–1347.

    Article  MathSciNet  MATH  Google Scholar 

  • Klink, P. C., van Ee, R., Nijs, M. M., Brouwer, G. J., Noest, A. J., & van Wezel, R. J. A. (2008). Early interactions between neuronal adaptation and voluntary control determine perceptual choices in bistable vision. J. Vis., 8(5), 16.1.

    Article  Google Scholar 

  • Laing, C. R., & Chow, C. C. (2002). A spiking neuron model for binocular rivalry. J. Comput. Neurosci., 12(1), 39–53.

    Article  Google Scholar 

  • Lankheet, M. J. M. (2006). Unraveling adaptation and mutual inhibition in perceptual rivalry. J. Vis., 6(4), 304–310.

    Article  Google Scholar 

  • Leopold, D. A., Wilke, M., Maier, A., & Logothetis, N. K. (2002). Stable perception of visually ambiguous patterns. Nat. Neurosci., 5(6), 605–609.

    Article  Google Scholar 

  • Levelt, W. J. M. (1965). On binocular rivalry. Institute for Perception RVO–TNO, Soesterberg, The Netherlands.

  • Moreno-Bote, R., Rinzel, J., & Rubin, N. (2007). Noise-induced alternations in an attractor network model of perceptual bistability. J. Neurophysiol., 98(3), 1125–1139.

    Article  Google Scholar 

  • Moreno-Bote, R., Shpiro, A., Rinzel, J., & Rubin, N. (2010). Alternation rate in perceptual bistability is maximal at and symmetric around equi-dominance. J. Vis., 10(11), 1.1.

    Article  Google Scholar 

  • Mueller, T., & Blake, R. (1989). A fresh look at the temporal dynamics of binocular rivalry. Biol. Cybern., 61, 223–232.

    Article  Google Scholar 

  • Noest, A. J., van Ee, R., Nijs, M. M., & van Wezel, R. J. A. (2007). Percept-choice sequences driven by interrupted ambiguous stimuli: a low-level neural model. J. Vis., 7(8), 10.1.

    Article  Google Scholar 

  • Orbach, J., Ehrlich, D., & Heath, H. A. (1963). Reversibility of the Necker cube. I. An examination of the concept of “satiation of orientation.” Percept. Mot. Skills, 17, 439–458.

    Article  Google Scholar 

  • Pearson, J., & Brascamp, J. (2008). Sensory memory for ambiguous vision. Trends Cogn. Sci., 12(9), 334–341.

    Article  Google Scholar 

  • Seely, J., & Chow, C. C. (2011). Role of mutual inhibition in binocular rivalry. J. Neurophysiol., 106(5), 2136–2150.

    Article  Google Scholar 

  • Shpiro, A., Curtu, R., Rinzel, J., & Rubin, N. (2007). Dynamical characteristics common to neuronal competition models. J. Neurophysiol., 97(1), 462–473.

    Article  Google Scholar 

  • Suzuki, S., & Grabowecky, M. (2002). Evidence for perceptual “trapping” and adaptation in multistable binocular rivalry. Neuron, 36(1), 143–157.

    Article  Google Scholar 

  • Taylor, A. L., Cottrell, G. W., & Kristan, W. B. Jr. (2002). Analysis of oscillations in a reciprocally inhibitory network with synaptic depression. Neural Comput., 14(3), 561–581.

    Article  MATH  Google Scholar 

  • van Ee, R. (2011). Percept-switch nucleation in binocular rivalry reveals local adaptation characteristics of early visual processing. J. Vis., 11(2), 13.1.

    Google Scholar 

  • Wang, X. J., & Rinzel, J. (1992). Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Comput., 4(1), 84–97.

    Article  Google Scholar 

  • Webster, M. A. (2011). Adaptation and visual coding. J. Vis., 11(5), 2.1.

    Article  Google Scholar 

  • Wilson, H. R. (2003). Computational evidence for a rivalry hierarchy in vision. Proc. Natl. Acad. Sci. USA, 100(24), 14499–14503.

    Article  Google Scholar 

  • Wilson, H. R., Blake, R., & Lee, S. H. (2001). Dynamics of travelling waves in visual perception. Nature, 412(6850), 907–910.

    Article  Google Scholar 

  • Wolfe, J. M. (1986). Stereopsis and binocular rivalry. Psychol. Rev., 93(3), 269–282.

    Article  Google Scholar 

Download references

Acknowledgements

S.J. was supported by an NSF Research Experience for Undergraduates Fellowship (EMSW21-RTG 0739261). Z.P.K. is supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship (DMS-1004422).

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Suren Jayasuriya & Zachary P. Kilpatrick

Authors
  1. Suren Jayasuriya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zachary P. Kilpatrick
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zachary P. Kilpatrick.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jayasuriya, S., Kilpatrick, Z.P. Effects of Time-Dependent Stimuli in a Competitive Neural Network Model of Perceptual Rivalry. Bull Math Biol 74, 1396–1426 (2012). https://doi.org/10.1007/s11538-012-9718-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-012-9718-0

Keywords

Search

Navigation