Krishnagopal Sanjukta, Lehnert Judith, Poel Winnie, Zakharova Anna, Schöll Eckehard
Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
Department of Physics, Birla Institute for Technology and Science Pilani, Pilani, Goa 403726, India.
Philos Trans A Math Phys Eng Sci. 2017 Mar 6;375(2088). doi: 10.1098/rsta.2016.0216.
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'.
我们研究了具有分形连接性的耦合斯图尔特 - 朗道振荡器网络中的复杂同步模式，如簇同步和部分振幅死亡。对分形或自相似拓扑结构的研究源于大脑中的神经元网络。这种分形特性在层次网络中得到了很好的体现，我们为此提出了三种不同的模型。此外，我们引入了一种解析本征解方法，并全面描述了网络拓扑与相应网络动力学之间的相互作用，从而使我们能够通过分析小的网络基序来预测任意大型层次网络的动力学。我们还表明，即使耦合是对称的，这些网络中也能诱导出振荡死亡，这与之前对振荡死亡的理解相反。我们的结果表明，拓扑结构与动力学之间存在直接关联：层次网络呈现出相应的层次动力学。这有助于弥合中尺度基序与宏观网络之间的差距。本文是主题为“控制论物理学前沿”的特刊的一部分。
