Phase jumps near a phase synchronization transition in systems of two coupled chaotic oscillators

Phase synchronization transitions in two different coupled chaotic systems (Rossler 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 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] similar to -(epsilon(c) - epsilon)(1/2), while away from the transition [l] similar to (epsilon(r) - epsilon)(-1/2) for both systems. [S0031-9007(98)06625-3].