Basin stability for burst synchronization in small-world networks of chaotic slow-fast oscillators

Maslennikov, Oleg V.; Nekorkin, Vladimir I.; Kurths, Jürgen

doi:10.1103/physreve.92.042803

Cited by 24 publications

(13 citation statements)

References 32 publications

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“…Among other limitations as vehicle through which to estimate network connectivity, Pearson correlation will fail to identify phase-synchronized time series oscillating at different frequencies, and we do not yet have reason to believe that network-pairs “communicate” or couple only within extremely well-matched spectral regimes. At the neural level, for example, phase synchrony is still utilized as a central indicator of coupling strength [1, 2] even though different cell types are known to have different natural rates of firing [3]. The activation patterns captured by fMRI are at a much coarser spatial and temporal scale than multi-electrode neuronal recordings.…”

Section: Introductionmentioning

confidence: 99%

Cross-Frequency rs-fMRI Network Connectivity Patterns Manifest Differently for Schizophrenia Patients and Healthy Controls

Miller

Yaesoubi

Calhoun

2016

IEEE Signal Process. Lett.

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Patterns of resting state fMRI functional network connectivity in schizophrenia patients have been shown to differ markedly from that of healthy controls. While some studies have explored connectivity within fixed frequency bands, the question of network phase synchrony across disparate frequency bands, or cross-frequency connectivity, has remained surprisingly underexplored. Computational modeling at the neuronal scale however has long acknowledged the existence of coupled fast and slow subsystems. Here we present preliminary evidence that cross-frequency coupling exists at the network level, that it patterns in meaningful ways over functional domains, and that this patterning differs between the healthy population and individuals with diagnosed schizophrenia.

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Section: Introductionmentioning

confidence: 99%

Cross-Frequency rs-fMRI Network Connectivity Patterns Manifest Differently for Schizophrenia Patients and Healthy Controls

Miller

Yaesoubi

Calhoun

2016

IEEE Signal Process. Lett.

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“…The basins stability method has been used to identify three mechanisms which create the circulating power flows. Moreover, one can find significant number of studies that use basin stability method to show the way to increase the efficiency of power grids [2,42,43,83] Maslennikov et al [61] study the basin stability of the burst synchronization regime in small-world networks consisting of chaotic slow-fast oscillators. The results confirm that the coupling density and the coupling strength influence the basin stability similarly and there are threshold values above which the basin stability of the burst synchronization regime significantly increase.…”

Section: Applicationsmentioning

confidence: 99%

“…To calculate basin stability measure one has to perform a significant number of Bernoulli trials and classify the final solutions reached in each trial. Proposed idea has been successfully applied to asses the stability of power grids [63,85], systems with time delay [56], chimera states [79], stabilization of saddle fixed points in coupled oscillators [78] and brain dynamics [61]. In our previous papers we proposed extensions of this method [12].…”

Section: Introductionmentioning

confidence: 99%

Sample-Based Methods of Analysis for Multistable Dynamical Systems

Brzeski

Perlikowski

2018

Arch Computat Methods Eng

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In this paper we present how sample based analysis can complement classical methods for analysis of dynamical systems. We describe how sample based algorithms can be utilized to obtain better understanding of complex dynamical phenomena, especially in multistable dynamical systems that are difficult for analytical investigations. Relying on the simple, direct numerical integration algorithms we are able to detect all possible solutions including hidden and rare attractors; investigate the ranges of stability in multiple parameters space; analyse the influence of parameters mismatch or model imperfections; assess the risk of dangerous or unwanted behaviour and reveal the structure of multidimensional phase space. For each mentioned application we present methodology, example on paradigmatic non-linear dynamical system and discuss practical applications. The presented methods of analysis can be applied to solve numerous of scientific problems originating from different disciplines. Moreover, their robustness and efficiency will grow with the upcoming increase of computational power.

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“…Here noise can give rise to a form of dynamics reminiscent of mixed-mode oscillations, cf. So far, models similar to (2) have been applied to address a number of problems associated to collective phenomena in networks of coupled neurons, including synchronization of electrically coupled units with spike-burst activity [49,50], pattern formation in complex networks with modular architecture [13,14,51], transient cluster activity in evolving dynamical networks [16], as well as the basin stability of synchronization regimes in smallworld networks [15]. Within this paper, the collective motion will be described in terms of the global variables…”

Section: Map Neuron Dynamics and The Population Modelmentioning

confidence: 99%

Mean-field dynamics of a population of stochastic map neurons

et al. 2017

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We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking, and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series. The effective model is further shown to reproduce with sufficient accuracy the phase response curves of the exact system and the assembly's response to external stimulation of finite amplitude and duration.

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Basin stability for burst synchronization in small-world networks of chaotic slow-fast oscillators

Cited by 24 publications

References 32 publications

Cross-Frequency rs-fMRI Network Connectivity Patterns Manifest Differently for Schizophrenia Patients and Healthy Controls

Cross-Frequency rs-fMRI Network Connectivity Patterns Manifest Differently for Schizophrenia Patients and Healthy Controls

Sample-Based Methods of Analysis for Multistable Dynamical Systems

Mean-field dynamics of a population of stochastic map neurons

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