Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany.
Department of Applied Mechanics, Budapest University of Technology and Economics, H-1111, Budapest, Hungary.
Phys Rev E. 2018 Jan;97(1-1):012311. doi: 10.1103/PhysRevE.97.012311.
Synchronization in networks of identical oscillators with heterogeneous coupling delays is studied. A decomposition of the network dynamics is obtained by block diagonalizing a newly introduced adjacency lag operator which contains the topology of the network as well as the corresponding coupling delays. This generalizes the master stability function approach, which was developed for homogenous delays. As a result the network dynamics can be analyzed by delay differential equations with distributed delay, where different delay distributions emerge for different network modes. Frequency domain methods are used for the stability analysis of synchronized equilibria and synchronized periodic orbits. As an example, the synchronization behavior in a system of delay-coupled Hodgkin-Huxley neurons is investigated. It is shown that the parameter regions where synchronized periodic spiking is unstable expand when increasing the delay heterogeneity.
研究了具有异质耦合时滞的相同振荡器网络中的同步。通过块对角化新引入的邻接滞后算子来获得网络动力学的分解，该算子包含网络的拓扑结构以及相应的耦合时滞。这推广了主稳定性函数方法，该方法是为齐次时滞开发的。因此，可以通过具有分布时滞的时滞微分方程来分析网络动力学，其中不同的网络模式出现不同的时滞分布。频域方法用于同步平衡点和同步周期轨道的稳定性分析。作为一个例子，研究了延迟耦合 Hodgkin-Huxley 神经元系统中的同步行为。结果表明，当增加延迟异质性时，同步周期尖峰不稳定的参数区域会扩展。
