Criticality and partial synchronization analysis in Wilson-Cowan and Jansen-Rit neural mass models

Abstract

Synchronization is a phenomenon observed in neuronal networks involved in diverse brain activities. Neural mass models such as Wilson-Cowan (WC) and Jansen-Rit (JR) manifest synchronized states. Although they have been studied for decades, their ability to demonstrate second-order phase transition (SOPT) and criticality has not received enough attention, which serves as candidates for the development of healthy brain networks. In this study, two networks of coupled WC and JR nodes with small-world topologies were constructed and Kuramoto order parameter (KOP) was used to quantify the amount of synchronization. In addition, we investigated the presence of SOPT using the synchronization coefficient of variation. Both networks reached high synchrony by changing the coupling weight between their nodes. Moreover, they exhibited abrupt changes in the synchronization at certain values of the control parameter not necessarily related to a phase transition. While SOPT was observed only in JR model, neither WC nor JR model showed power-law behavior. Our study further investigated the global synchronization phenomenon that is known to exist in pathological brain states, such as seizure. JR model showed global synchronization, while WC model seemed to be more suitable in producing partially synchronized patterns. Corresponding author summaryYousef Jamali received his M.Sc. degree in physics from Sharif University, Tehran, Iran, in 2004, and his Ph.D. degree in physics from Sharif University, Tehran, Iran, in 2009. After finishing his Ph.D. thesis, in 2009, he got two years postdoctoral research associate position at the University of California at Berkeley, Department of Bioengineering. He is currently an Associate Professor in the Applied Mathematics Department (Biomathematics division), at Tarbiat Modares University, Tehran, Iran. His current research interests include the interdisciplinary area of the complex system especially on the modeling of brain. In fact, his interests are how the brain works at the critical state and how this complex system synchronized under different conditions.