An active system 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 insta_bility 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.
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