a frame co-rotating with the drive. Hence this stable fixed point represents a state in which the order parameter is moving periodically while staying phase-locked to the drive. Therefore, back in the original frame, a macroscopic fraction of the oscillator population must also be moving in rigid synchrony, locked to the same frequency as the drive signal.

### Region B: Bistability between two states of forced entrainment

Now suppose we weaken the forcing. Imagine moving down along a vertical line in Fig. 1(b), decreasing $F$ while holding $\Omega$ fixed. As we do so, we first pass from region A into the extremely narrow region B by crossing through the upper branch of the saddle-node curve . At this bifurcation, a stable node is born out of the vacuum, along with a saddle point. Meanwhile, the stable fixed point that we encountered in Region A still exists; it lies in the lower right part of Fig. 2(b).

Thus Region B depicts a form of bistability. Depending on the initial conditions, the system chooses one of two possible states of forced entrainment, differing in their phase coherence (the magnitude of $z$) and their phase relationship to the drive signal (the argument of 