One can see in Fig. 7 that the solutions found using the reduced system based on the deterministic center manifold compare poorly with the original system at very low noise values. Furthermore, as the noise increases, the agreement between the two solutions gets worse. On the other hand, Fig. 7 shows that the solutions computed using the reduced system found using the normal form coordinate transform compare very well with the solutions to the original system across a wide range of small noise intensities.