A note on the statistical dynamics of two mutually phase-locked oscillators

This note demonstrates that the behavior of two mutually synchronized phase-locked oscillators using delay compensation is equivalent to that of a first-order loop with the loop parameters degraded by the residual uncompensated delays of the system. In particular, the probability density of phase differences between the two oscillators is derived and the numerical results are also presented. The cycle slipping rate is easily obtained from this density.