NOISE-INDUCED TRANSITION OF A SELF-SUSTAINED OSCILLATOR

A model noisy oscillator system is investigated stochastically by anal yzing the transient properties of two deterministic attractors. It is found that after prolonged perturbation by large noise, the limit cycl e is deformed from its deterministic shape, and that the deformation o ccurs mostly near the region where the self-sustaining mechanism preva ils. The trivial fixed point ceases to be a steady state in the stocha stic sense, and turns into a metastable state with increasing variance s. This metastable state, which repels all phase paths not initiating from itself, is found to attract all trajectories that detour from the deformed limit cycle. The expected transition from the limit cycle to an erratic oscillation via the metastable state is characterized by a simple power law. The corresponding exponent is numerically determine d over a broad range of initial configurations and rate constants.