Wang Xingang, Zhou Cangtao, Lai Choy Heng
Temasek Laboratories, National University of Singapore, 117508 Singapore.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 2):056208. doi: 10.1103/PhysRevE.77.056208. Epub 2008 May 16.
Recent studies have shown that the synchronizability of complex networks can be significantly improved by gradient or asymmetric couplings, and increase of the gradient strength could enhance the network synchronizability monotonically. Here we argue and demonstrate that, for a typical complex network, there could be an optimal gradient where the maximum network synchronizability is achieved. That is, large gradient may deteriorate synchronization. We attribute the suppressing effect of gradient coupling to the phenomenon of network breaking and show that, comparing with sparse homogeneous networks, dense heterogeneous networks suffer less from network breaking and, consequently, benefit more from large gradient in improving synchronization. The findings are supported by indirect simulations of eigenvalue analysis and direct simulations of coupled nonidentical oscillators.
最近的研究表明，复杂网络的同步性可通过梯度或非对称耦合得到显著改善，且梯度强度的增加可单调增强网络同步性。在此我们论证并表明，对于一个典型的复杂网络，可能存在一个最优梯度，在该梯度下可实现最大网络同步性。也就是说，过大的梯度可能会使同步性变差。我们将梯度耦合的抑制作用归因于网络破裂现象，并表明，与稀疏均匀网络相比，密集异质网络受网络破裂的影响较小，因此，在改善同步性方面从大梯度中获益更多。这些发现得到了特征值分析间接模拟和耦合非相同振荡器直接模拟的支持。
