Synchronization patterns: from network motifs to hierarchical networks

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 pr...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2017-03, Vol.375 (2088), p.20160216-20160216
Main Authors: Krishnagopal, Sanjukta, Lehnert, Judith, Poel, Winnie, Zakharova, Anna, Schöll, Eckehard
Format: Article
Language:English
Subjects:
Brain
Cybernetics
Death
Dynamics
Fractal Topology
Fractals
Hierarchical Networks
Network topologies
Networks
Oscillation Death
Oscillators
Partial Synchronization
Self-similarity
Synchronism
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Summary: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. This article is part of the themed issue ‘Horizons of cybernetical physics’.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.2016.0216