We have investigated the oscillator death behavior on small-world networks. On one hand, we find that small-world connectivity can eliminate the oscillator death present in the regular lattice. On the other hand, the small-world connectivity can also lead to global oscillator death which is absent in the regular lattice or the completely random network.

• Received 9 July 2003

DOI:https://doi.org/10.1103/PhysRevE.68.055103