Dynamics of chaotic maps for modelling the multifractal spectrum of human brain Diffusion Tensor Images

Provata, A.; Katsaloulis, P.; Verganelakis, Dimitrios

doi:10.1016/j.chaos.2011.11.009

Cited by 30 publications

(16 citation statements)

References 20 publications

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“…Even in globally coupled networks chimera states have been ob-served [49,50,40]. A further type of coupling is inspired by recent findings in neuroscience, which revealed an inhomogeneous, fractal-like (hierarchical) topology of neurons in the human brain [51,52,53,54,55]. For such hierarchical, quasi-fractal connectivities chimera states have also been observed recently in various time-continuous systems [24,29,56,57,58].…”

Section: Introductionmentioning

confidence: 96%

Chimera states in networks of logistic maps with hierarchical connectivities

et al. 2018

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Chimera states are complex spatiotemporal patterns consisting of coexisting domains of coherence and incoherence. We study networks of nonlocally coupled logistic maps and analyze systematically how the dilution of the network links influences the appearance of chimera patterns. The network connectivities are constructed using an iterative Cantor algorithm to generate fractal (hierarchical) connectivities. Increasing the hierarchical level of iteration, we compare the resulting spatiotemporal patterns. We demonstrate that a high clustering coefficient and symmetry of the base pattern promotes chimera states, and asymmetric connectivities result in complex nested chimera patterns.PACS. PACS-key discribing text of that key -PACS-key discribing text of that key

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Section: Introductionmentioning

confidence: 96%

Chimera states in networks of logistic maps with hierarchical connectivities

et al. 2018

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“…Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) studies revealed an intricate architecture in the neuron interconnectivity of the human and mammalian brain: the connectivity of the neuron axons network represents a hierarchical (quasi-fractal) geometry. [73][74][75][76][77] Motivated by these studies, the goal of the present manuscript is to analyze different networks with a hierarchical connectivity and systematically explore the mechanisms of a) stefan.ulonska@fu-berlin.de b) schoell@physik.tu-berlin.de formation of chimera states in such networks. Note that these quasi-fractal coupling topologies have hierarchical structure, although they differ from the hierarchical tree-like models widely studied in the network science.…”

Section: Introductionmentioning

confidence: 99%

Chimera states in networks of Van der Pol oscillators with hierarchical connectivities

Ulonska

Omelchenko

Zakharova

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

106

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Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We analyse chimera states in ring networks of Van der Pol oscillators with hierarchical coupling topology. We investigate the stepwise transition from a nonlocal to a hierarchical topology and propose the network clustering coefficient as a measure to establish a link between the existence of chimera states and the compactness of the initial base pattern of a hierarchical topology; we show that a large clustering coefficient promotes the occurrence of chimeras. Depending on the level of hierarchy and base pattern, we obtain chimera states with different numbers of incoherent domains. We investigate the chimera regimes as a function of coupling strength and nonlinearity parameter of the individual oscillators. The analysis of a network with larger base pattern resulting in larger clustering coefficient reveals two different types of chimera states and highlights the increasing role of amplitude dynamics.

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“…So far oscillation death has been described as the result of symmetry breaking [27,44,45]. Here, we demonstrate that oscillation death can also occur in symmetric networks with symmetric coupling when the collective frequency of the oscillators tends to zero.On the topological side, we focus on hierarchical networks exhibiting a fractal or self-similiar structure [46][47][48][49][50], which is motivated by the intricate architecture found in neural networks: Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) results show that neurons in the mammal brain are far from being linked homogeneously but are connected in a fractal manner, with fractal dimensions varying between 2.3 and 2.8, depending on local properties, on the subject, and on the noise reduction threshold [46,[51][52][53][54]. Other examples of fractal networks include protein interaction networks [55] or biochemical reactions in the metabolism [56] and hyperlinks in the World Wide Web [57].Ground-breaking work connecting the topological properties of a network with its dynamics has been done by Pecora et al in introducing the master stability function for the completely synchronous state [58].…”

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confidence: 99%

Synchronization patterns: from network motifs to hierarchical networks

Krishnagopal

Lehnert

Poel

et al. 2017

Phil. Trans. R. Soc. A.

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One contribution of 15 to a theme issue 'Horizons of cybernetical physics' . We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is motivated by the network of neurons in the brain. This fractal property is well represented in hierarchical networks, for which we present three different models. In addition, we introduce an analytical eigensolution method and provide a comprehensive picture of the interplay of network topology and the corresponding network dynamics, thus allowing us to predict the dynamics of arbitrarily large hierarchical networks simply by analysing small network motifs. We also show that oscillation death can be induced in these networks, even if the coupling is symmetric, contrary to previous understanding of oscillation death. Our results show that there is a direct correlation between topology and dynamics: hierarchical networks exhibit the corresponding hierarchical dynamics. This helps bridge the gap between mesoscale motifs and macroscopic networks. Subject Areas: complexity KeywordsThis article is part of the themed issue 'Horizons of cybernetical physics'.

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Dynamics of chaotic maps for modelling the multifractal spectrum of human brain Diffusion Tensor Images

Cited by 30 publications

References 20 publications

Chimera states in networks of logistic maps with hierarchical connectivities

Chimera states in networks of logistic maps with hierarchical connectivities

Chimera states in networks of Van der Pol oscillators with hierarchical connectivities

Synchronization patterns: from network motifs to hierarchical networks

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