For stochastic model reduction, there exist several potential methods for general problems. For a system with certain spectral requirements, the existence of a stochastic center manifold was proven in Ref. 18 . Nonrigorous stochastic normal form analysis ͑which leads to the stochastic center mani-fold͒ was performed in Refs. [19] [20] [21] [22] . Rigorous theoretical analysis of normal form coordinate transformations for stochastic center manifold reduction was developed in Refs. 23 and 24. Later, another method of stochastic normal form reduction was developed, 25 in which any anticipatory convolutions ͑integrals into the future of the noise processes͒ that appeared in the slow modes were removed. Since this latter analysis makes the construction of the stochastic normal form coordinate transform more transparent, we use this method to derive the reduced stochastic center manifold equation. Figure 1 shows a schematic demonstrating our approach to the problem. We consider a high-dimensional system along with its corresponding reduced low-dimensional system. In this article, two types of low-dimensional system are discussed: a reduced system based on deterministic center manifold analysis and a reduced system based on a stochastic normal form coordinate transform. Regardless of the type of low-dimensional system being considered, a common noise is injected into both the high-dimensional and lowdimensional models, and an analysis of the solutions found using the high and low-dimensional systems is performed.