Nonlinear modeling of multistable perception

NEWSLETTER OF THE SOCIETY FOR CHAOS THEORY IN PSYCHOLOGY & LIFE SCIENCES, 2020

We discuss a computational model that describes the stabilization of percept choices under intermittent viewing of an ambiguous visual stimulus at long stimulus intervals (Toff). Unlike previous studies we incorporate the time that the stimulus is on (Ton) and Toff explicitly as parameters of the mathematical model of the perceptual choices. These parameters are then used as two bifurcation parameters of the problem. Using the new GUI environment of the MATLAB software package MatCont we elucidate the bifurcations of periodic orbits responsible for switching between alternating and repetitive sequences. We show that the stability borders in the parameter plane of the alternating and repeating sequences consist of curves of limit point and period-doubling bifurcations of periodic orbits. The stability regions overlap resulting in a wedge with bistability of both sequences. We conclude by comparing our results with the results obtained by direct numerical simulation in a grid of (Toff,Ton) values in the 2007 paper of Noest, van Ee, Nijs and van Wezel.

Encyclopedia of Computational Neuroscience, 2014

Multistability in Perception Dynamics is the phenomenon of spontaneous switching in the subject's perception between different interpretations of an ambiguous sensory stimulus.

Journal of Experimental Psychology: Human Perception and Performance, 1993

Biological Cybernetics, 2014

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.

PLoS Computational Biology, 2009

We propose a novel explanation for bistable perception, namely, the collective dynamics of multiple neural populations that are individually meta-stable. Distributed representations of sensory input and of perceptual state build gradually through noise-driven transitions in these populations, until the competition between alternative representations is resolved by a threshold mechanism. The perpetual repetition of this collective race to threshold renders perception bistable. This collective dynamics -which is largely uncoupled from the time-scales that govern individual populations or neuronsexplains many hitherto puzzling observations about bistable perception: the wide range of mean alternation rates exhibited by bistable phenomena, the consistent variability of successive dominance periods, and the stabilizing effect of past perceptual states. It also predicts a number of previously unsuspected relationships between observable quantities characterizing bistable perception. We conclude that bistable perception reflects the collective nature of neural decision making rather than properties of individual populations or neurons. Citation: 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.

Perceptual Bistability refers to the phenomenon of spontaneously switching between two or more interpretations of an image under continuous viewing. Although switching behavior is increasingly well characterized, the origins remain elusive. We propose that perceptual switching naturally arises from the brain's search for best interpretations while performing Bayesian inference. In particular, we propose that the brain explores a posterior distribution over image interpretations at a rapid time scale via a sampling-like process and updates its interpretation when a sampled interpretation is better than the discounted value of its current interpretation. We formalize the theory, explicitly derive switching rate distributions and discuss qualitative properties of the theory including the effect of changes in the posterior distribution on switching rates. Finally, predictions of the theory are shown to be consistent with measured changes in human switching dynamics to Necker cube stimuli induced by context. * http://www.schrater.org

2013

The present work addresses a particular problem that humans and other animals need to deal with while making their way through their environments. The environment always affords much more possibilities for action than one could engage in. How does an animal become attuned to one property of the environment and then switch to another one when the circumstances begin to change? What happens when one forces a human participant in an environment as much deprived of possibilities for action as could be possible? The conceptual and mathematical tools of dynamical systems theory and synergetics allow a good expression of the applicable ecological theory. The switches are phase transitions. Phase transitions imply instabilities. In all circumstances an instability is induced by breaking the loop of perceiving and acting, the circular coupling spanning a perceptual system, an action system, and the environment. In the first pair of experiments, we find that diminishing the action availability is responsible for negative hysteresis in an affordance boundary paradigm. Negative hysteresis is a phenomenon that offers a look one layer deeper into the dynamics of self-organized systems. In the second pair of experiments, we find that the same logic helps explain a classical phenomenon in vision science. The spontaneous switches between modes of perception observed with certain types of displays have the character of an instability. Under the conditions of constant Dobromir Georgiev Dotov -University of Connecticut, 2013 environment deprived of possibilities for action the perceptual system enters a dynamical regime with no stable solution but only transiently stable alternating attractors.

2017

Modern studies in physiology and cognitive neuroscience consider a noise as an important constructive factor of the brain functionality. Under the adequate noise, the brain can rapidly access different ordered states, and provide decision-making by preventing deadlocks. Bistable dynamic models are often used for the study of the underlying mechanisms of the visual perception. In the present paper, we consider a bistable energy model subject to both additive and parametric noise. Using the catastrophe theory formalism and stochastic sensitivity functions technique, we analyze a response of the equilibria to noise, and study noiseinduced transitions between equilibria. We demonstrate and analyse the effect of hysteresis squeezing when the intensity of noise is increased. Stochastic bifurcations connected with the suppression of oscillations by parametric noises are discussed.

2015

We have studied the temporal characteristics of bistable perception of the stimuli of two types: one involves alterations in a perceived depth and another one has an ambiguous content. We used the Necker lattice and lines of shadowed circles ambiguously perceived either as spheres or holes as stimuli of the first type. The Winson figure (the Eskimo/Indian picture) was a stimulus of the second type. We have analyzed how often the reversals occurred (reversal rate) and for how long each of the two interpretations, or percepts, was observed during one presentation (stability durations). For all three ambiguous images the reversal rate and the stability durations had similar values, which provide another evidence for a significant role of top-down processes in multistable perception. Keywords—Multistable perception, perceived depth, reversal rate, top-down processes.

Journal of Computational Neuroscience, 2014

The phenomenon of perceptual multistability in which alternate interpretations of a fixed stimulus are perceived intermittently is an active area of research and the underlying mechanisms that gate perception are little understood. Numerical tools from bifurcation analysis are applied to the study of a competition model posed as a feature-only neural field equation. In the absence of input the model with a spikefrequency adaptation mechanism has been shown to produce an array of complex spatio-temporal dynamics local to a Bogdanov-Takens point. Here, we demonstrate how, with the introduction of an input, the organisation of solutions in parameter space changes via symmetry breaking. The model is then used to investigate a more complex stimulus in the context of motion integration that is multistable in terms of its perceived direction of motion, the so-called multistable barber pole, which has been the subject of concurrent psychophysics experiments. We bring the model to an operating regime where known physiological response properties are reproduced whilst also working close to bifurcation. We find that in this regime the model is able to account for characteristic behaviour from experiment in terms of the type of switching observed and changes in the rate of switching with respect to contrast. In this way, the modelling study sheds light on the underlying mechanisms that drive perceptual switching in different contrast regimes. The general approach presented is applicable to a broad range of perceptual competition problems in which spatial interactions play a role.