title: Synchronization patterns: from network motifs to hierarchical networks.
abstract: 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'.
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany sanju33@gmail.com.|Department of Physics, Birla Institute for Technology and Science Pilani, Pilani, Goa 403726, India.
authors.forename: Sanjukta
authors.initials: S
authors.lastname: Krishnagopal
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany.
authors.forename: Judith
authors.identifier: http://orcid.org/0000-0003-3372-207X
authors.initials: J
authors.lastname: Lehnert
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany.
authors.forename: Winnie
authors.initials: W
authors.lastname: Poel
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany.
authors.forename: Anna
authors.initials: A
authors.lastname: Zakharova
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany.
authors.forename: Eckehard
authors.initials: E
authors.lastname: Schöll
keywords: fractal topology; hierarchical networks; oscillation death; partial synchronization