In addition to computing the cross correlation between the solution of the original system and the solutions of the two reduced systems for i = 0.0005, we have computed the cross correlation for the case of zero noise as well as for noise intensities ranging from = 5.0ϫ 10 −10 to = 5.0ϫ 10 −5 . These cross correlations were computed using time series from t = 800 to t = 1000. For the deterministic case ͑zero noise͒, the cross correlation between the time series which were computed using the original system and the reduced system based on the deterministic center manifold is 1.0, since the agreement is perfect. The cross correlation between the original system and the reduced system found using the stochastic normal form is also 1.0. Figure 7 shows the cross correlation between the original system and the two reduced systems for various values of .