Diverse self-sustained oscillatory patterns and their mechanisms in excitable small-world networks.

Diverse self-sustained oscillatory patterns and their mechanisms in small-world networks (SWNs) of excitable nodes are studied. Spatiotemporal patterns of SWNs are sensitive to long-range connection probability P and coupling intensity D . By varying P in wide range with fixed D , we observe totally six types of asymptotic states: pure spiral waves, pure self-sustained target waves, patterns of mixtured spirals and target waves, pseudospiral turbulence, synchronizing oscillations, and rest state. The parameter conditions for all these states are specified, and the mechanisms of these states are heuristically explained. In particular, the mechanism of emergence and annihilation of synchronizing oscillations is explained by using the shortest path length analysis.