By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kind of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network. Interestingly, it is found that by increasing a parameter that governs the weight distribution, the onset of synchronization in WDC network is monotonically enhanced, while in WDU network there is a reverse in the synchronization performance. We investigate this phenomenon from the viewpoint of gradient network, and explain the contrary roles of coupling gradient on network synchronization: gradient promotes synchronization in WDC network, while deteriorates synchronization in WDU network. The findings highlight the fact that, besides the link weight, the correlation between the weight and node degree is also important to the network dynamics.
A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase oscillators in which the links mediating the interactions are constantly rearranged with a characteristic timescale and, possibly, an extremely low instantaneous connectivity. We show that, provided strong coupling and fast enough rewiring are considered, the network is able to reach partial synchronization even in the vanishing connectivity limit. We also provi…
Complex transitions to synchronization in delay-coupled networks of logistic maps
一个网络的延迟耦合逻辑映射表现出两种不同的同步制度，这取决于耦合延迟时间的分布。当延迟在整个网络中是均匀的时，网络将进入时间依赖状态[Atay et al.，物理修订信函92，144101（2004）]，根据延迟的不同，它可能是周期性的或混乱的;当延迟足够不均匀时，同步进入稳态，这对于非耦合映射来说是不稳定的[Masoller和Marti，Phys. Rev. Lett. 94，134102（2005）]。在这里，我们的特点的过渡依赖于时间的稳定状态的同步延迟分布的宽度增加。我们还比较了两个过渡到同步的耦合强度的增加。我们使用通过符号分析和有序模式计算的转移概率。我们发现，随着耦合强度的增加，在稳态同步开始之前，网络分裂成两个集群，这是在反相关系与对方。另一方面，随着延迟异质性的增加，没有团簇形成被认为是在稳态同步的开始，然而，一个相当复杂的非同步状态被检测到，揭示了在网络节点的转移概率的多样性。
We investigate transition to synchronization in Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage ($f$) of higher degree nodes of the network are assumed to be correlated with their degrees and that of the remaining nodes are drawn from some standard distribution namely Lorenz distribution. The effects of variation of $f$ and phase frustration parameter $α$ on transition to synchronization are investigated in detail. Self-consistent equations involving critical coupling strength ($λ_c$) and group angular velocity ($Ω_c$) …
