Dahms Thomas, Lehnert Judith, Schöll Eckehard
Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 2):016202. doi: 10.1103/PhysRevE.86.016202. Epub 2012 Jul 5.
We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability approach, we find that the master stability function shows a discrete rotational symmetry depending on the number of groups. The coupling matrices that permit solutions on group or cluster synchronization manifolds show a very similar symmetry in their eigenvalue spectrum, which helps to simplify the evaluation of the master stability function. Our theory allows for the characterization of stability of different patterns of synchronized dynamics in networks with multiple delay times, multiple coupling functions, but also with multiple kinds of local dynamics in the networks' nodes. We illustrate our results by calculating stability in the example of delay-coupled semiconductor lasers and in a model for neuronal spiking dynamics.
我们研究了延迟耦合网络中同步状态的稳定性，其中同步发生在具有不同局部动力学的组中，或者发生在具有相同局部动力学的网络中的簇状态。使用主稳定性方法，我们发现主稳定性函数根据组的数量显示出离散的旋转对称性。允许在组或簇同步流形上有解的耦合矩阵在其特征值谱中显示出非常相似的对称性，这有助于简化主稳定性函数的评估。我们的理论允许对具有多个延迟时间、多个耦合函数以及网络节点中多种局部动力学的网络中不同同步动力学模式的稳定性进行表征。我们通过计算延迟耦合半导体激光器示例中的稳定性以及神经元脉冲发放动力学模型中的稳定性来说明我们的结果。
