Impact of bistability in the synchronization of chaotic maps with delayed coupling and complex topologies

We investigate the impact of bistability in the emergence of synchronization in networks of chaotic maps with delayed coupling. The existence of a single finite attractor of the uncoupled map is found to be responsible for the emergence of synchronization. No synchronization is observed when the local dynamics has two competing chaotic attractors whose orbits are dense on the same interval. This result is robust for regular networks with variable ranges of interaction and for more complex topologies.