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Criticality and partial synchronization analysis in Wilson-Cowan and Jansen-Rit neural mass models
Sheida Kazemi1, AmirAli Farokhniaee2, Yousef Jamali1
1Biomathematics Laboratory, Department of Applied Mathematics, School of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran.
This study explored synchronization in Wilson-Cowan (WC) and Jansen-Rit (JR) neural models. The Jansen-Rit model showed second-order phase transitions and global synchronization, unlike the WC model.
Area of Science:
- Computational Neuroscience
- Complex Systems
Background:
- Neuronal networks exhibit synchronization crucial for brain function.
- Neural mass models like Wilson-Cowan (WC) and Jansen-Rit (JR) simulate synchronized states.
- The potential for second-order phase transitions (SOPT) and criticality in these models is under-explored.
Purpose of the Study:
- To investigate second-order phase transitions (SOPT) and criticality in coupled WC and JR neural networks.
- To quantify synchronization using the Kuramoto order parameter (KOP).
- To explore global synchronization patterns relevant to pathological brain states.
Main Methods:
- Constructed coupled WC and JR networks with small-world topologies.
- Quantified synchronization using the Kuramoto order parameter (KOP).
- Assessed SOPT using the synchronization coefficient of variation.
Main Results:
- Both WC and JR networks achieved high synchrony with increased coupling.
- The Jansen-Rit (JR) model exhibited second-order phase transitions (SOPT).
- Neither model displayed power-law behavior; JR showed global synchronization, while WC produced partial synchronization.
Conclusions:
- The Jansen-Rit (JR) model demonstrates second-order phase transitions (SOPT) and global synchronization, offering insights into brain dynamics.
- The Wilson-Cowan (WC) model is better suited for modeling partially synchronized patterns.
- Further research is needed to fully understand criticality in neural mass models.
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