Forced synchronization of coupled oscillators

We consider a system of coupled two oscillators with external force. At fir st we introduce the symmetrical property of the system. When the external f orce is not applied, the two oscillators are synchronized at the opposite p hase. We obtain a bifurcation diagram of periodic solutions in the coupled system when the single oscillator has a stable anti-phase solution. We find that the synchronized oscillations eventually become in-phase when the amp litude of the external force is increased.