Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

Budzinski, Roberto C.; Boaretto, B. R. R.; Prado, Thiago de Lima; Lopes, S. R.

doi:10.3390/mca24020042

Cited by 4 publications

(6 citation statements)

References 71 publications

(158 reference statements)

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“…Both models exhibited a transition from an unsynchronized to a highly synchronized state. This kind of behavior was detected in ensembles of coupled oscillators [47,[66][67][68]. A similar occurrence of transition from unsynchronized to full phase synchronized state is observed in [59].…”

Section: Resultssupporting

confidence: 69%

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

Kazemi,

Farokhniaee,

Jamali

2023

Preprint

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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.

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Section: Resultssupporting

confidence: 69%

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

Kazemi,

Farokhniaee,

Jamali

2023

Preprint

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“…Nodes can interact with each other and generate different dynamics behaviors. Changing the coupling coefficient between nodes and analysis of network dynamics has received interest recently 51 , 54 , 55 .…”

Section: Resultsmentioning

confidence: 99%

“…Since synchronization is an appropriate measurement for neural dynamics, it has appeared as an ordered parameter in many research 51 – 57 . In brain networks, the coupling strength between units 54 , 55 and the amount of external input of nodes 49 , 58 , 59 are two interesting parameters to be analyzed. Indeed, neural mass models can show different behaviors due to these parameters, and initial conditions vary in each run.…”

Section: Introductionmentioning

confidence: 99%

Phase synchronization and measure of criticality in a network of neural mass models

Kazemi

Jamali

2022

Sci Rep

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Synchronization has an important role in neural networks dynamics that is mostly accompanied by cognitive activities such as memory, learning, and perception. These activities arise from collective neural behaviors and are not totally understood yet. This paper aims to investigate a cortical model from this perspective. Historically, epilepsy has been regarded as a functional brain disorder associated with excessive synchronization of large neural populations. Epilepsy is believed to arise as a result of complex interactions between neural networks characterized by dynamic synchronization. In this paper, we investigated a network of neural populations in a way the dynamics of each node corresponded to the Jansen–Rit neural mass model. First, we study a one-column Jansen–Rit neural mass model for four different input levels. Then, we considered a Watts–Strogatz network of Jansen–Rit oscillators. We observed an epileptic activity in the weak input level. The network is considered to change various parameters. The detailed results including the mean time series, phase spaces, and power spectrum revealed a wide range of different behaviors such as epilepsy, healthy, and a transition between synchrony and asynchrony states. In some points of coupling coefficients, there is an abrupt change in the order parameters. Since the critical state is a dynamic candidate for healthy brains, we considered some measures of criticality and investigated them at these points. According to our study, some markers of criticality can occur at these points, while others may not. This occurrence is a result of the nature of the specific order parameter selected to observe these markers. In fact, The definition of a proper order parameter is key and must be defined properly. Our view is that the critical points exhibit clear characteristics and invariance of scale, instead of some types of markers. As a result, these phase transition points are not critical as they show no evidence of scaling invariance.

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“…Nodes can interact with each other and generate different dynamics behaviors. Changing the coupling coefficient between nodes and analysis of network dynamics has been interested recently 35,38,39 .…”

Section: Resultsmentioning

confidence: 99%

“…Neural mass models have a long history. Lopez da silva 30,31 , Jansen and Rit 32,33 , Wendling 34,35 , Wilson-Cowan [36][37][38][39] , Freeman [40][41][42] , and Wong-Wang 43,44 are some models that investigated the collective behavior of neurons. These models are…”

Section: Introductionmentioning

confidence: 99%

Phase synchronization and criticality in a network of neural mass models

Kazemi

Jamali

2021

Preprint

View full text Add to dashboard Cite

Synchronization has an important role in neural networks, and their dynamics are mostly accompanied by cognitive activities such as memory, learning, and perception. These activities arise from the collective neural behaviors and are not totally understood yet. This paper aims to investigate a cortical model from this perspective. In this paper, we investigated a network of neural populations in a way the dynamics of each node corresponded to the Jansen-Rit neural mass model. First, we put this dynamic on a single mass of four different input levels. Then, we considered a Watts-Strogatz network of Jansen-Rit oscillators. We observed an epileptic activity in the weak input level. The network to change various parameters is considered. The detailed results including the mean times series, phase spaces and power spectrum revealed a wide range of different behaviors such as epilepsy, unimpaired, and a transition between synchrony and asynchrony states. Since the critical state is a dynamic candidate for healthy brains, we considered some measures of criticality and investigated them on phase transition points. We showed that the criticality hypothesis is not all or nothing theory. It means that due to the nature of specific indicators selected for studying the criticality, the phase transition point can be a critical point or not. Indeed, some markers of criticality can exist in phase transition points, and others may not. As a result, we do not claim that neural models show criticality or not, but we can only admit that they have a percentage of criticality.

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Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

Cited by 4 publications

References 71 publications

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

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

Phase synchronization and measure of criticality in a network of neural mass models

Phase synchronization and criticality in a network of neural mass models

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