A model system of relaxation oscillator is investigated stochastically, by treating the perturbation of random driving as white noise added to rate equations. We analyze noise effects on transient processes before and after a limit cycle is attained. Noise renders speeding-up effect when the cycle is approached from outside. Relaxation from inside is slowing-down, especially in a region near the trivial point attractor. These opposite tendencies are enhanced by noise intensity, and cease to exist after the cycle is reached. The point attractor remains a fixed point in stochastic analysis. The limit cycle is found to be noise-robust since the period is invariant and the trajectory preserves practically the same structure. Deviations from a deterministic shape occur mostly near the turning points of oscillation. For large noise and after prolonged perturbations, the limit cycle deforms significantly and shows tendency to spiral towards a point attractor. Stochastic characteristcs of this phenonenon are analyzed in detail.
