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Volume 2017 (2017), Article ID 4391587, 14 pages
Research Article

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

1University of Warsaw, Stefana Banacha 2, 02-097 Warsaw, Poland
2Donders Institute for Brain, Cognition and Behavior, Kapittelweg 29, 6525 EN Nijmegen, Netherlands
3Radboud University Nijmegen Medical Centre, Geert Grooteplein Zuid 10, 6525 GA Nijmegen, Netherlands
4Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Ks. Trojdena 4, 02-109 Warsaw, Poland

Correspondence should be addressed to Natalia Z. Bielczyk

Received 26 May 2017; Revised 15 July 2017; Accepted 25 July 2017; Published 6 September 2017

Academic Editor: Fathalla A. Rihan

Copyright © 2017 Urszula Foryś et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.