Phase synchronization transitions in two different coupled chaotic systems (Rössler and Lorentz) are investigated and shown to be well described by a reduced model of an overdamped periodically driven nonlinear oscillator with a time varying coefficient. In both systems, the phase separation increases with $2\pi$ phase jumps below the transition. The scaling rules of the jump near and away from the transition are studied: Near the transition the average interval between two successive jumps follows $\ln 〈l〉\sim -({\epsilon }_c-\epsilon {)}^{1/2}$, while away from the transition $〈l〉\sim ({\epsilon }_t-\epsilon {)}^{-1\mathrm{}/2}$ for both systems.

• Received 30 January 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.321