Onset of synchronization in systems of globally coupled chaotic maps

We study the transition to coherence of an ensemble of globally coupled chaotic maps allowing for ensembles of nonidentical maps and for noise. The transition coupling strength is determined from a kind of transfer function of the perturbation evolution. We present analytical results, and we test these results using numerical experiments for several large systems consisting of ensembles of many coupled maps. The later includes ensembles of identical noiseless maps, identical maps subject to noise, and ensembles of nonidentical maps. One of our examples suggests that the validity of the perturbation theory approach can be problematic for an ensemble of noiseless identical maps if the maps are nonhyperbolic. However, for such a case, noise and/or parameter spread seems to have a regularizing effect restoring the validity of perturbation theory.