Alternating Locking Ratios in Imperfect Phase Synchronization

In periodically driven chaotic dynamical systems with a broad distribution of intrinsic time scales,perfect phase synchronization cannot be reached. Long segments of evolution during which the phaseof a chaotic variable follows the phase of the driving force are interrupted by short segments of phasedrift. We demonstrate that this drift is another short-lived synchronized state; its onset is caused by thepassage near the long unstable periodic orbits whose frequencies are locked by external force in ratiosdifferent from 1:1. [S0031-9007(99)09190-5]