Oscillatory transient regime in the forced dynamics of a nonlinear auto oscillator

We demonstrate that the forced transient dynamics of a nonlinear (nonisochronous) auto-oscillator is qualitatively different from the dynamics of a quasilinear oscillator described by the classical Adler's model. If the normalized amplitude mu of the driving force exceeds a certain critical value mu(cr), the transition to the synchronized regime becomes oscillatory with a frequency proportional to proportional to root mu-mu(cr) and a synchronization time that is almost independent of mu. The discovered effect is illustrated on the example of a strongly nonlinear spin torque nano-oscillator (STNO) where the finite transient synchronization time can limit the possible range of STNO modulation frequencies.