Irrational phase synchronization.

We study the occurrence of physically observable phase locked states between chaotic oscillators and rotors in which the frequencies of the coupled systems are irrationally related. For two chaotic oscillators, the phenomenon occurs as a result of a coupling term which breaks the 2 pi invariance in the phase equations. In the case of rotors, a coupling term in the angular velocities results in very long times during which the coupled systems exhibit alternatively irrational phase synchronization and random phase diffusion. The range of parameters for which the phenomenon occurs contains an open set, and is thus physically observable.