STOCHASTIC TRANSIENT OF A RELAXATION-OSCILLATOR

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 bef ore and after a limit cycle is attained. Noise renders speeding-up eff ect when the cycle is approached from outside. Relaxation from inside is slowing-down, especially in a region near the trivial point attract or. These opposite tendencies are enhanced by noise intensity, and cea se to exist after the cycle is reached. The point attractor remains a fixed point in stochastic analysis. The limit cycle is found to be noi se-robust since the period is invariant and the trajectory preserves p ractically the same structure. Deviations from a deterministic shape o ccur mostly near the turning points of oscillation. For large noise an d after prolonged perturbations, the limit cycle deforms significantly and shows tendency to spiral towards a point attractor. Stochastic ch aracteristcs of this phenonenon are analyzed in detail.