Impact of Time Delay in Perceptual Decision-Making: Neuronal Population Modeling Approach

Abstract

Impairments in decision-making are frequently observed in neurodegenerative diseases, but the mechanisms underlying such pathologies remain elusive. In this work, we study, on the basis of novel time-delayed neuronal population model, if the delay in self-inhibition terms can explain those impairments. Analysis of proposed system reveals that there can be up to three positive steady states, with the one having the lowest neuronal activity being always locally stable in nondelayed case. We show, however, that this steady state becomes unstable above a critical delay value for which, in certain parameter ranges, a subcritical Hopf bifurcation occurs. We then apply psychometric function to translate model-predicted ring rates into probabilities that a decision is being made. Using numerical simulations, we demonstrate that for small synaptic delays the decision-making process depends directly on the strength of supplied stimulus and the system correctly identifies to which population the stimulus was applied. However, for delays above the Hopf bifurcation threshold we observe complex impairments in the decision-making process; that is, increasing the strength of the stimulus may lead to the change in the neuronal decision into a wrong one. Furthermore, above critical delay threshold, the system exhibits ambiguity in the decision-making.

Time-delay model of perceptual decision making in cortical networks

“…We model these delays through Delayed Differential Equations (DDEs). DDEs are often used to model biological systems [20, 32, 47–54] because they exhibit a rich dynamical repertoire, and in particular, they fall into oscillatory regime on the edge of instability. DDEs were also used in the neural mass and neural field models of cortical activity [55–59].…”

“…In this work, we investigate a winner-take-all population model with delayed local inhibition to characterize perceptual switches in the binary decision making. We have proposed this model in our previous work [20]. In this work, we investigated mathematical properties of this model, especially with respect to the influence of the value of inhibitory delays on the emergence of temporal switches in the decision making.…”

Time-delay model of perceptual decision making in cortical networks

“…But how do the oscillations 48 arise? Some hint was given by Deco et al [13] who demonstrated in a simulation study that 49 a network of nodes with sigmoidal transfer functions, coupled with transmission delays, can 50 start oscillating in the gamma range when tuned to a subcritical state.…”

“…DDEs are often used to model biological systems [27,[41][42][43][44][45][46][47][48][49] because they exhibit a rich 311 dynamical repertoire, and in particular, they fall into oscillatory regime on the edge of instability. 312 DDEs were also used in the neural mass and neural field models of cortical activity [50][51][52][53][54].…”