Note that Eq. ͑28a͒ is the deterministic center manifold equation, and at first order, matches the center manifold equation that was found previously ͓Eq. ͑17͔͒. Substitution of Y = 0 and neglecting all multiplicative noise terms and memory integrals using the argument from above ͑so that we consider only first-order noise terms͒ leads to the following reduced system of evolution equations on the center manifold: