Self-oscillations and critical fluctuations

An active system is analyzed whose parameter space contains a bistable region of stationary states bounded by a cuspidal point. This point is somewhat analogous to the critical point of a non-symmetry-breaking phase transition (in terms of high low-frequency susceptibility, fluctuation growth, etc.). The system has not only stationary states, but also periodic oscillatory ones. When parameters change so that the oscillatory instability threshold passes through the cuspidal point, the continuous spectrum of fluctuations transforms into the discrete spectrum of periodic oscillations. The dynamics associated with this transformation are examined.