Computer simulations of spin waves parametric excitations are carried out in the framework of the two modes model. The dependence of the auto-oscillation (AO) frequency, f, on the pumping amplitude h is investigated. The results support the expression of Lvov et al. for this dependence in cases when the parametric excitation threshold, hth is very close to the auto-oscillation threshold hosc. In cases when hosc is considerably larger than hth, a much better fit is obtained to a slightly modified expression: f = f0 + B([h/hosc]2 -1)0.5 where f0 is the onset frequency and B is a constant. Support is given to the idea of Lvov et al. that auto oscillation evolves from an oscillation that is damped below hosc and becomes self sustained at hosc. We find that τCO, the decay time of AO below hosc exhibits a critical slowing down power law: τCO ∝ (1 - h/hosc)-2.2. The dependence of f on the inter mode interaction strengths when h is constant, satisfies the expression: f = D + C/(E + 2T11 + S11 + 2T12 + S12) where D, C, and E are constants and T11 T12, S11, and S12 are the inter mode interaction strengths. This result supports the conjecture that the dependence of the auto-oscillation frequency on the physical parameters is very similar to that of N0, the steady state value of the total number of parametric excitations.