The relationship between the topology and synchronizability of partially interdependent networks

Abstract

Based on the master stability function method, some theoretical results are derived for the synchronizability of partially interdependent networks. For bounded and unbounded synchronous regions and three different kinds of inter-coupling, we illustrate how factors of the topology can affect the synchronizability of networks with a Barabási-Albert (BA) scale-free and a Newman-Watts (NW) small-world subnet (simplified here as BA-NW network) and networks with a BA scale-free and a nearest-neighbor (NN) subnet (BA-NN network), respectively. When only the scale of the networks is increased, the synchronizability systematically reduces. If only increasing the inter-coupling strength or the number of interdependent nodes, the synchronizability keeps improving. Generally, we find that BA-NW networks have better synchronizability than BA-NN networks and positively correlated coupling is the best interconnection. Random inter-coupling, by contrast, is the best choice for BA-NN networks.

Analysis of the synchronizability of two-layer chain networks with two inter-layer edges

“…本章分别针对前文所提定理及三个猜想进行数值模拟仿真, 以验证其合理性. 上述利用主稳定方法得到的结论与文献 [28] 中利用牵制控制的同步准则得出的关于链状网络最重 要 2 个节点的节点组的结论具有一致性, 异曲同工. Figure 3 Varying λ 2 versus inter-layer coupling strength a for all the possible "inter-layer i&j connection" modes for X = 20.…”

Finite‐time optimal pinning control and synchronization for partially interdependent networks

“…In recent years, researches on synchronization and control for interdependent networks or “networks of networks” have been started 29‐37 . Reference 29 explored the synchronization of networks consisting of many subnetworks by using pinning control technology.…”

“…Taking the “surveillance‐control” system as an example, Reference 32 discussed the controllability of interdependent networks and pointed out that the reliability of control equipment was very important for network control. Reference 33 probed the relationship between the topological structure and the synchronizability of partially interdependent networks. Reference 34 analyzed the process from node to node synchronization to complete the synchronization for multilayer networks.…”