NOISE-INDUCED TRANSITION OF A SELF-SUSTAINED OSCILLATOR

A model noisy oscillator system is investigated stochastically by analyzing the transient properties of two deterministic attractors. It is found that after prolonged perturbation by large noise, the limit cycle is deformed from its deterministic shape, and that the deformation occurs mostly near the region where the self-sustaining mechanism prevails. The trivial fixed point ceases to be a steady state in the stochastic sense, and turns into a metastable state with increasing variances. 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 determined over a broad range of initial configurations and rate constants.