Origin of amplitude synchronization in coupled nonidentical oscillators

Qiu, Qi; Zhou, Benzheng; Wang, Pai; He, Li; Xiao, Yunhao; Zhen-yu, Yang; Zhan, Meng

doi:10.1103/physreve.101.022210

Cited by 11 publications

(6 citation statements)

References 39 publications

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“…Until recently, a proper understanding of the relation between amplitude and phase related measures has been lacking, and the assumption was that amplitude correlations would arise in the context of stronger coupling. However, using the same Stuart Landau model as in the present study, Qiu et al ( 2020 ) were able to show that amplitude envelope correlations can be caused by weak coupling between oscillators with slightly different frequencies in the absence of noise and before the onset of phase synchronization.…”

Section: Discussionmentioning

confidence: 46%

“…3 . The choice to study these two coupling measures is motivated by the fact that amplitude correlations and phase coherence/synchronization probably reflect two fundamentally different modes of communication in brain networks (Engel et al 2013 ; Qiu et al 2020 ; Schoonhoven et al 2022 ; Siems and Siegel et al 2020 ). The amplitude envelope correlation is the Pearson correlation coefficient of the amplitude envelopes of pairs of channels, which can be obtained directly from the model as shown in formula [ 4 ].…”

Section: Methodsmentioning

confidence: 99%

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Network Hyperexcitability in Early Alzheimer’s Disease: Is Functional Connectivity a Potential Biomarker?

et al. 2023

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Network hyperexcitability (NH) is an important feature of the pathophysiology of Alzheimer’s disease. Functional connectivity (FC) of brain networks has been proposed as a potential biomarker for NH. Here we use a whole brain computational model and resting-state MEG recordings to investigate the relation between hyperexcitability and FC. Oscillatory brain activity was simulated with a Stuart Landau model on a network of 78 interconnected brain regions. FC was quantified with amplitude envelope correlation (AEC) and phase coherence (PC). MEG was recorded in 18 subjects with subjective cognitive decline (SCD) and 18 subjects with mild cognitive impairment (MCI). Functional connectivity was determined with the corrected AECc and phase lag index (PLI), in the 4–8 Hz and the 8–13 Hz bands. The excitation/inhibition balance in the model had a strong effect on both AEC and PC. This effect was different for AEC and PC, and was influenced by structural coupling strength and frequency band. Empirical FC matrices of SCD and MCI showed a good correlation with model FC for AEC, but less so for PC. For AEC the fit was best in the hyperexcitable range. We conclude that FC is sensitive to changes in E/I balance. The AEC was more sensitive than the PLI, and results were better for the thetaband than the alpha band. This conclusion was supported by fitting the model to empirical data. Our study justifies the use of functional connectivity measures as surrogate markers for E/I balance.

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Section: Discussionmentioning

confidence: 46%

Section: Methodsmentioning

confidence: 99%

Network Hyperexcitability in Early Alzheimer’s Disease: Is Functional Connectivity a Potential Biomarker?

et al. 2023

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“…This complementary phenomenon was not observed in the lower bands (theta and alpha), where we rather found increased AS but decreased PS, as quantified by increased IC-based features. While this behaviour might appear counter-intuitive, it nevertheless matches with the complex spectrum of configurations that mechanistically emerge from the interactions of oscillatory signals [56]. In neuroscience applications, it has been actually shown that there could be phase-coupling without amplitudecoupling and vice-versa [57].…”

Section: Mental State Detection In Single Individualsmentioning

confidence: 67%

Phase/Amplitude Synchronization of Brain Signals During Motor Imagery BCI Tasks

Cattai

Colonnese

Corsi

et al. 2021

IEEE Trans. Neural Syst. Rehabil. Eng.

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In the last decade, functional connectivity (FC) has been increasingly adopted based on its ability to capture statistical dependencies between multivariate brain signals. However, the role of FC in the context of brain-computer interface applications is still poorly understood. To address this gap in knowledge, we considered a group of 20 healthy subjects during an EEG-based hand motor imagery (MI) task. We studied two well-established FC estimators, i.e. spectral-and imaginarycoherence, and we investigated how they were modulated by the MI task. We characterized the resulting FC networks by extracting the strength of connectivity of each EEG sensor and we compared the discriminant power with respect to standard power spectrum features. At the group level, results showed that while spectral-coherence based network features were increasing in the sensorimotor areas, those based on imaginary-coherence were significantly decreasing. We demonstrated that this opposite, but complementary, behavior was respectively determined by the increase in amplitude and phase synchronization between the brain signals. At the individual level, we eventually assessed the potential of these network connectivity features in a simple offline classification scenario. Taken together, our results provide fresh insights into the oscillatory mechanisms subserving brain network changes during MI and offer new perspectives to improve BCI performance.

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“…( 1)w i t hf = f (z)=( ↵ + )z z|z| 2 , z 2 C and the coupling function h(•)=sin(•). The uncoupled system is the normal form for Hopf bifurcation and, therefore, plays an important role as a phenomenologic model for studying collective dynamics [11,24,26,33,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]. It possesses an equilibrium at the origin, which is asymptotically stable for ↵<0, and a stable periodic orbit for ↵>0, which emerges at the Hopf bifurcation for ↵ = 0.…”

Section: )mentioning

confidence: 99%

Stabilization of synchronous equilibria in regular dynamical networks with delayed coupling

2023

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We consider the synchronization problem of dynamical networks with delayed interactions. More specifically, we focus on the stabilization of synchronous equilibria in regular networks where the degrees of all nodes are equal. By studying such control near a Hopf bifurcation, we obtain necessary and sufficient conditions for stabilization. It is shown that the stabilization domains in the parameter space reappear periodically with time-delay. We find that the frequency of reappearance of the control domains is linearly proportional to the number of cycle multipartitions of the network. IntroductionDynamical networks with complex topology are a very powerful approach for the study of large complex systems in various application areas ranging from neuroscience, engineering, to sociology, economics or Earth sciences. From this perspective, real-world systems are modeled as networks of interacting nodes, where the nodes have their own dynamics and influence each other's behavior in complex ways [1][2][3][4][5]. Research in this area combines various application fields with theoretical approaches from dynamical system theory, statistical physics, time series analysis, or graph theory.The networks can range from a few to hundreds of billions of nodes, such as large communication networks or the brain. Connectivity in networks can vary widely, ranging from "all-to-all" to hierarchical or even sparse.When modeling realistic situations, time-delays must be often taken into account for the interactions in dynamical networks, as is the case in neural systems [6-9], laser networks [10-12], machine learning [13], traffic dynamics [14], and other applications. Particularly challenging are the situations in which the interplay between time-delays and network symmetries [15][16][17][18] or large delays [19-22] lead to new dynamical phenomena. They include synchronization [21,[23][24][25][26][27][28][29][30], explosive synchronization [31,32], various resonances [33], chimera states [24,34] and other patterns [35][36][37][38][39].The interplay between network topology and time-delayed interactions are also explored in [40,41].Many natural systems possess unstable states, and the stabilization of them might be of interest for applications. For example, stabilization of unstable equilibrium solution has application in semiconductor lasers [42], in nanoeletronics [43], in medicine [44], and others. An efficient strategy to control unstable periodic orbits, which is also applied to stabilization of equilibrium, is introducing a self-feedback delayed term. This approach is non-invasive, since the feedback term does not alter the original solutions. In particular, for stabilization of periodic orbits, the usual approach is to consider the delay equal or close to the period of the orbit, known as Pyragas control [45]. For stabilization of equilibrium, the aim can also be achieved with a suitable choice of delay [46,47].Here we consider a network model in which the nodes are interacting with a common time-delay.Hence, the delay is not an...

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Origin of amplitude synchronization in coupled nonidentical oscillators

Cited by 11 publications

References 39 publications

Network Hyperexcitability in Early Alzheimer’s Disease: Is Functional Connectivity a Potential Biomarker?

Network Hyperexcitability in Early Alzheimer’s Disease: Is Functional Connectivity a Potential Biomarker?

Phase/Amplitude Synchronization of Brain Signals During Motor Imagery BCI Tasks

Stabilization of synchronous equilibria in regular dynamical networks with delayed coupling

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