Mechanism of Synchronization in Frequency Dividers

We investigate the mechanism leading to synchronization in injection-locked frequency dividers using methods of asymptotic analysis. We introduce a response function which allows for qualitative evaluation and intuitive interpretation of the locking phenomenon. We show that the linear asymptotic approximation predicts the locking intervals with high accuracy for a class of models and parameter sets reported in the literature. The accuracy of the approach is evaluated by comparing the theoretical prediction with numerical results. We use phase space analysis to study the case where the limit cycle is dominated by a strongly anharmonic oscillation.