Forced synchronization of a delayed-feedback oscillator

Dynamics of a delayed-feedback oscillator with cubic nonlinearity driven by an external harmonic signal is considered. Regimes of forced synchronization and their stability conditions are studied analytically and numerically for the cases of single-frequency and multiple-frequency (self-modulation) operation of the free-running oscillator. Special attention is paid to synchronization of the oscillator with bistability of steady states which arises near the boundary of generation zone. Results of numerical simulation of bifurcation transitions to synchronization regime for different driving frequencies are presented. Main differences from the classical picture of synchronization for a system with one degree of freedom are discussed.