$z$).

### Region C: Bistability between forced entrainment and phase trapping

Continuing our vertical descent through Fig. 1(b), we next cross from B into C by passing through the curve of Hopf bifurcations, Eq. . The stable fixed point created in Region B now loses stability and gives birth to a tiny attracting limit cycle (Fig. 2(c)). On this cycle the order parameter still runs at the same average frequency as the drive but its relative phase and amplitude now wobble slightly. Because these variations remain trapped within tight limits, one says the system is phase trapped (as opposed to phase locked) to the drive. Back in the original non-rotating frame, the macroscopic dynamics for this state would be quasiperiodic with two frequencies. This is not the only attractor, of course; the state of forced entrainment seen earlier in A and B persists, so we still have bistability, but now between phase trapping and forced entrainment.

### Region D: Forced entrainment

Passing from Region C to D carries us across a curve of homoclinic bifurcations. As we approach this curve from above, the tiny limit cycle in Fig. 2(c) expands. At the bifurcation it touches the saddle point and forms 