Phase synchronization in coupled chaotic systems: Transitions from high- to low-dimensional chaos

Phase synchronization in coupled chaotic systems is an interesting topic in recent years on nonlinear dynamics. Phase synchronization implies an order ed behavior embedded in chaotic motions. Recent progress on phase synchroni zations is reviewed. The synchronization process is exhibited by applying t he bifurcation tree. The synchronization process is identified as transitio ns from high-to low-dimensional chaos. An alternative phase locking among v arious rational ratios is found. Chaos suppression and the restoration to c haos synchronization via period-doubling is studied. It is found that asymm etric coupling can greatly enhance the phase synchronization of coupled osc illators.