Son Seung-Woo, Jeong Hawoong, Hong Hyunsuk
Department of Physics, Institute for the BioCentury, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 2):016106. doi: 10.1103/PhysRevE.78.016106. Epub 2008 Jul 14.
We study collective synchronization in a large number of coupled oscillators on various complex networks. In particular, we focus on the relaxation dynamics of the synchronization, which is important from the viewpoint of information transfer or the dynamics of system recovery from a perturbation. We measure the relaxation time tau that is required to establish global synchronization by varying the structural properties of the networks. It is found that the relaxation time in a strong-coupling regime (K>Kc) logarithmically increases with network size N , which is attributed to the initial random phase fluctuation given by O(N-1/2) . After elimination of the initial-phase fluctuation, the relaxation time is found to be independent of the system size; this implies that the local interaction that depends on the structural connectivity is irrelevant in the relaxation dynamics of the synchronization in the strong-coupling regime. The relaxation dynamics is analytically derived in a form independent of the system size, and it exhibits good consistency with numerical simulations. As an application, we also explore the recovery dynamics of the oscillators when perturbations enter the system.
我们研究了各种复杂网络上大量耦合振子中的集体同步。特别地，我们关注同步的弛豫动力学，从信息传递或系统从扰动中恢复的动力学角度来看，这一点很重要。我们通过改变网络的结构特性来测量建立全局同步所需的弛豫时间τ。结果发现，在强耦合 regime（K>Kc）中，弛豫时间随网络规模N呈对数增加，这归因于由O(N-1/2)给出的初始随机相位波动。消除初始相位波动后，发现弛豫时间与系统规模无关；这意味着在强耦合 regime中，依赖于结构连通性的局部相互作用在同步的弛豫动力学中是无关紧要的。弛豫动力学以一种与系统规模无关的形式进行了解析推导，并且与数值模拟表现出良好的一致性。作为一个应用，我们还探索了扰动进入系统时振子的恢复动力学。
