Partial Phase Cohesiveness in Networks of Networks of Kuramoto Oscillators

Qin, Yuzhen; Kawano, Yu; Portoles, Oscar; Cao, Ming

doi:10.1109/tac.2021.3062005

“…Remark 7: Here, we discuss differences between our result and those in [25], where partial phase cohesiveness within clusters is considered with a slightly different setting. In this paper we consider the perturbation of the edge weights from an external equitable partition.…”

Section: Practical Stability Without External Equitable Partitionsmentioning

confidence: 78%

“…However, cluster synchronization of Kuramoto oscillators has not been deeply studied except for [23], [24]. A slightly different definition of cluster synchronization was employed in [25], where phase cohesiveness within clusters was explored. On the other hand, some authors considered cluster synchronization problems for general nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Cluster Synchronization of Kuramoto Oscillators and Brain Functional Connectivity

Kato¹,

Ishii²

2022

Preprint

0

View full text Add to dashboard Cite

The recent progress of functional magnetic resonance imaging techniques has unveiled that human brains exhibit clustered correlation patterns of their spontaneous activities. It is important to understand the mechanism of cluster synchronization phenomena since it may reflect the underlying brain functions and brain diseases. In this paper, we investigate cluster synchronization conditions for networks of Kuramoto oscillators. The key analytical tool that we use is the method of averaging, and we provide a unified framework of stability analysis for cluster synchronization. The main results show that cluster synchronization is achieved if (i) the inter-cluster coupling strengths are sufficiently weak and/or (ii) the natural frequencies are largely different among clusters. Moreover, we apply our theoretical findings to empirical brain networks. Discussions on how to understand brain functional connectivity and further directions to investigate neuroscientific questions are provided.

show abstract

“…The role of structural connectivity for generating specific coordination patterns was first brought to light by GWBMs of resting-state dynamics [19]. In a previous study we have shown analytically that the strength of structural connectivity plays an important role in selectively coordinating regions by means of modulations of local connectivity strength [46]. Additionally, structural symmetries and time-delays might have influenced dpFC in our simulations [19,47,48].…”

Section: Discussionmentioning

confidence: 96%

Thalamic bursts modulate cortical synchrony locally to switch between states of global functional connectivity in a cognitive task

Portoles

¹

,

Blesa

²

,

Vugt

³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Performing a cognitive task requires going through a sequence of functionally diverse stages. Although it is typically assumed that these stages are characterized by distinct states of cortical synchrony that are triggered by sub-cortical events, little reported evidence supports this hypothesis. To test this hypothesis, we first identified cognitive stages in single-trial MEG data of an associative recognition task, showing with a novel method that each stage begins with local modulations of synchrony followed by a state of directed functional connectivity. Second, we developed the first whole-brain model that can simulate cortical synchrony throughout a task. The model suggests that the observed synchrony is caused by thalamocortical bursts at the onset of each stage, targeted at cortical synapses and interacting with the structural anatomical connectivity. These findings confirm that cognitive stages are defined by distinct states of cortical synchrony and explains the network-level mechanisms necessary for reaching stage-dependent synchrony states.

show abstract

“…The role of structural connectivity in generating specific coordination patterns was first brought to light by GWBMs of resting-state dynamics [ 22 ]. In a previous study we have shown analytically that the strength of structural connectivity plays an important role in selectively coordinating regions by means of modulations of local connectivity strength [ 46 ]. Additionally, structural symmetries and time delays might have influenced dpFC in our simulations [ 22 , 47 , 48 ].…”

Section: Discussionmentioning

confidence: 99%

Thalamic bursts modulate cortical synchrony locally to switch between states of global functional connectivity in a cognitive task

Portoles

¹

,

Blesa

²

,

Vugt

³

et al. 2022

Self Cite

View full text Add to dashboard Cite

Performing a cognitive task requires going through a sequence of functionally diverse stages. Although it is typically assumed that these stages are characterized by distinct states of cortical synchrony that are triggered by sub-cortical events, little reported evidence supports this hypothesis. To test this hypothesis, we first identified cognitive stages in single-trial MEG data of an associative recognition task, showing with a novel method that each stage begins with local modulations of synchrony followed by a state of directed functional connectivity. Second, we developed the first whole-brain model that can simulate cortical synchrony throughout a task. The model suggests that the observed synchrony is caused by thalamocortical bursts at the onset of each stage, targeted at cortical synapses and interacting with the structural anatomical connectivity. These findings confirm that cognitive stages are defined by distinct states of cortical synchrony and explains the network-level mechanisms necessary for reaching stage-dependent synchrony states.

show abstract

Partial Phase Cohesiveness in Networks of Networks of Kuramoto Oscillators

Cited by 18 publications

References 31 publications

Cluster Synchronization of Kuramoto Oscillators and Brain Functional Connectivity

Cluster Synchronization of Kuramoto Oscillators and Brain Functional Connectivity

Thalamic bursts modulate cortical synchrony locally to switch between states of global functional connectivity in a cognitive task

Thalamic bursts modulate cortical synchrony locally to switch between states of global functional connectivity in a cognitive task

Contact Info

Product

Resources

About