Phase-Locked and Phase-Drift Solutions of Phase Oscillators with Asymmetric Coupling Strengths

Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths and inhomogeneous natural frequencies. The solutions exhibit interesting profiles of the phase lags resulting from the pacemaker corresponding to the ratio of upward and downward coupling strengths. Using the existence condition of phase-locked solutions, the transition points from phase-locked to phase-drift states are evaluated. The application of the existence condition to the case of the linear gradient of the natural frequency illustrates some scaling properties in the frequency diagrams.