Physics Department, Lehigh University, Bethlehem, Pennsylvania 18015, USA.
Chaos. 2011 Jun;21(2):025111. doi: 10.1063/1.3595601.
We study the clusterization of phase oscillators coupled with delay in complex networks. For the case of diffusive oscillators, we formulate the equations relating the topology of the network and the phases and frequencies of the oscillators (functional response). We solve them exactly in directed networks for the case of perfect synchronization. We also compare the reliability of the solution of the linear system for non-linear couplings. Taking advantage of the form of the solution, we propose a frequency adaptation rule to achieve perfect synchronization. We also propose a mean-field theory for uncorrelated random networks that proves to be pretty accurate to predict phase synchronization in real topologies, as for example, the Caenorhabditis elegans or the autonomous systems connectivity.
我们研究了具有时滞的耦合相振子在复杂网络中的聚类。对于扩散振子的情况，我们构建了网络拓扑与振子的相位和频率（功能响应）之间的关系方程。我们在有向网络中对完美同步的情况进行了精确求解。我们还比较了非线性耦合线性系统解的可靠性。利用解的形式，我们提出了一种频率自适应规则来实现完美同步。我们还提出了一种用于非相关随机网络的平均场理论，该理论证明对于预测真实拓扑中的相位同步非常准确，例如，秀丽隐杆线虫或自主系统的连通性。
