Background: 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) can simulate 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.
Objective & methods: Two networks of coupled WC and JR nodes with small-world topologies were constructed and Kuramoto order parameter was used to quantify the amount of synchronization. In addition, we investigated the presence of critical states using synchronization coefficient of variation.
Results: Both networks reached to 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. SOPT was observed only in JR model associated with a critical point.
Conclusion: Synchronization with high variability is a necessary, but not enough condition for SOPT and one needs to find an associated critical point for further verification. Critical points in networks of dynamical systems exhibit characteristics that are invariant, and our findings study could advance our understanding of brain disorders such as the absence of seizure activity at low frequencies.

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