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Chunk #27 — Results and discussion — Synchronization in interconnected networks

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Effective Subnetwork Topology for Synchronizing Interconnected Networks of Coupled Phase Oscillators.
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We also investigate how the choice of connector nodes influences synchrony in NoNs of various subnetwork topologies. Here the synchrony alignment function is used to analyze r for NoNs constructed by connecting the lowest-degree nodes, instead of the highest-degree nodes, in two subnetworks. Natural frequencies are allocated randomly, and Kintra is increased to 12. The order parameters of the four topologies are summarized in Figure 4H, together with the results for the default case in which highest-degree nodes are used as connector nodes. The results show that the super-hub and SF topologies achieve highest synchrony even when the lowest-degree nodes are the connector nodes. Under this connection strategy, random networks exhibit the lowest synchrony, which is primarily due to a stochastic existence of nodes with very few intra-subnetwork connections. Such nodes can appear in SF networks as well, but in SF networks, the node is likely to be directly coupled to a high-degree node, and hence the global synchrony does not degrade even when the low-degree node is used as a connector.