Bifurcation study of a neural field competition model with an application to perceptual switching in motion integration.

Perceptual multistability is a phenomenon in which alternate interpretations of a fixed stimulus are perceived intermittently. Although correlates between activity in specific cortical areas and perception have been found, the complex patterns of activity and the underlying mechanisms that gate multistable perception are little understood. Here, we present a neural field competition model in which competing states are represented in a continuous feature space. Bifurcation analysis is used to describe the different types of complex spatio-temporal dynamics produced by the model in terms of several parameters and for different inputs. The dynamics of the model was then compared to human perception investigated psychophysically during long presentations of an ambiguous, multistable motion pattern known as the barberpole illusion. In order to do this, the model is operated in a parameter range where known physiological response properties are reproduced whilst also working close to bifurcation. The model accounts for characteristic behaviour from the psychophysical experiments 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

The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down

The effects of noise on binocular rivalry waves: a stochastic neural field model

We analyse the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how multiplicative noise in the activity variables leads to a diffusive–like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. The multiplicative noise also renormalizes the mean speed of the wave. We use our analysis to calculate the first passage time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation leads to quenched disorder in the neural fields during propagation of a wave

The relative contribution of noise and adaptation to competition during tri-stable motion perception

Animals exploit antagonistic interactions for sensory processing and these can cause oscillations between competing states. Ambiguous sensory inputs yield such perceptual multi-stability. Despite numerous empirical studies using binocular rivalry or plaid pattern motion, the driving mechanisms behind the spontaneous transitions between alternatives remain unclear. In the current work, we used a tri-stable barberpole motion stimulus combining empirical and modelling approaches to elucidate the contributions of noise and adaptation to underlying competition. We first robustly characterised the coupling between perceptual reports of transitions and continuously recorded eye direction, identifying a critical window of 480ms before button presses within which both measures were most strongly correlated. Second, we identified a novel non monotonic relationship between stimulus contrast and average perceptual switching rate with an initially rising rate before a gentle reduction at higher contrasts. A neural fields model of the underlying dynamics introduced in previous theoretical work and incorporating noise and adaptation mechanisms was adapted, extended and empirically validated. Noise and adaptation contributions were confirmed to dominate at the lower, and higher, contrasts respectively. Model simulations with two free parameters, controlling adaptation dynamics and direction thresholds, captured the measured mean transition rates for participants. We verified the shift from noise dominated towards adaptation-driven in both the eye direction distributions and inter-transition duration statistics. This work combines modelling and empirical evidence to demonstrate the signal strength dependent interplay between noise and adaptation during tri- stability. We propose that the findings generalise beyond the barberpole stimulus case to ambiguous perception in continuous feature space

Changes of Mind in an Attractor Network of Decision-Making

Attractor networks successfully account for psychophysical and neurophysiological data in various decision-making tasks. Especially their ability to model persistent activity, a property of many neurons involved in decision-making, distinguishes them from other approaches. Stable decision attractors are, however, counterintuitive to changes of mind. Here we demonstrate that a biophysically-realistic attractor network with spiking neurons, in its itinerant transients towards the choice attractors, can replicate changes of mind observed recently during a two-alternative random-dot motion (RDM) task. Based on the assumption that the brain continues to evaluate available evidence after the initiation of a decision, the network predicts neural activity during changes of mind and accurately simulates reaction times, performance and percentage of changes dependent on difficulty. Moreover, the model suggests a low decision threshold and high incoming activity that drives the brain region involved in the decision-making process into a dynamical regime close to a bifurcation, which up to now lacked evidence for physiological relevance. Thereby, we further affirmed the general conformance of attractor networks with higher level neural processes and offer experimental predictions to distinguish nonlinear attractor from linear diffusion models

The relative contribution of noise and adaptation to competition during tri-stable motion perception

International audienceAnimals exploit antagonistic interactions for sensory processing and these can cause oscillations between competing states. Ambiguous sensory inputs yield such perceptual multi-stability. Despite numerous empirical studies using binocular rivalry or plaid pattern motion, the driving mechanisms behind the spontaneous transitions between alternatives remain unclear. In the current work, we used a tri-stable barberpole motion stimulus combining empirical and modelling approaches to elucidate the contributions of noise and adaptation to underlying competition. We first robustly characterised the coupling between perceptual reports of transitions and continuously recorded eye direction, identifying a critical window of 480ms before button presses within which both measures were most strongly correlated. Second, we identified a novel non monotonic relationship between stimulus contrast and average perceptual switching rate with an initially rising rate before a gentle reduction at higher contrasts. A neural fields model of the underlying dynamics introduced in previous theoretical work and incorporating noise and adaptation mechanisms was adapted, extended and empirically validated. Noise and adaptation contributions were confirmed to dominate at the lower, and higher, contrasts respectively. Model simulations with two free parameters, controlling adaptation dynamics and direction thresholds, captured the measured mean transition rates for participants. We verified the shift from noise dominated towards adaptation-driven in both the eye direction distributions and inter-transition duration statistics. This work combines modelling and empirical evidence to demonstrate the signal strength dependent interplay between noise and adaptation during tri- stability. We propose that the findings generalise beyond the barberpole stimulus case to ambiguous perception in continuous feature spaces

Perspectives on the Neuroscience of Cognition and Consciousness

The origin and current use of the concepts of computation, representation and information in Neuroscience are examined and conceptual flaws are identified which vitiate their usefulness for addressing problems of the neural basis of Cognition and Consciousness. In contrast, a convergence of views is presented to support the characterization of the Nervous System as a complex dynamical system operating in the metastable regime, and capable of evolving to configurations and transitions in phase space with potential relevance for Cognition and Consciousness

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Bifurcation analysis applied to a model of motion integration with a multistable stimulus

A computational study into the motion perception dynamics of a multistable psychophysics stimulus is presented. A diagonally drifting grating viewed through a square aperture is can be perceived as moving in the actual grating direction or in line with the aperture edges (horizontally or vertically). The different percepts are the product of interplay between ambiguous contour cues and specific terminator cues. We present a dynamical model of motion integration that performs direction selection for such a stimulus and link the different percepts to coexisting steady-states of the underlying equations. We apply the powerful tools of bifurcation analysis and numerical continuation to study the changes to the model's solution structure under the variation of parameters. Indeed, we apply these tools in a systematic way, taking into account biological and mathematical constraints, in order to fix model parameters. A region of parameter space is identified for which the model reproduces the qualitative behaviour observed in experiments. The temporal dynamics of motion integration are studied within this region; specifically, the effect of varying the stimulus gain is studied, which allows for qualitative predictions to be made