Best Spatiotemporal Performance Sustained by Optimal Number of Random Shortcuts on Complex Networks

The spatial synchronization and temporal coherence of FitzHugh--Nagumo (FHN) neurons on complex networks are numerically investigated. When an optimal number of random shortcuts are added to a regular neural chain, the system can reach a state which is nearly periodic in time and almost synchronized in space. More shortcuts do not increase the spatial synchronization too much, but will obviously destroy the temporal regularity.