Stability of mode locked states of coupled oscillator arrays

A method for analyzing beat frequency entrained (or mode locked) systems of coupled nonlinear oscillators is presented. Stable mode locked states are almost periodic oscillations that occur outside of the fundamental entrainment region of the array, and generate a periodic pulse train when the oscillator outputs are summed. The analysis relates the stability of the states to the relationship between the frequency pullings and the time average phases of the oscillators. The method is applied to three mode locked Van der Pol oscillators with arbitrary coupling time delay, and shows that the mode locking bandwidth is maximized for specific values of coupling delay and oscillator nonlinearity parameter.>