In order to make use of the center manifold theory, we must transform Eqs. ͑1a͒-͑1c͒ to a new system of equations that has the necessary spectral structure. The theory will allow us to find an invariant center manifold passing through the fixed point to which we can restrict the transformed system. Details regarding the transformation can be found in Sec. III A, and the computation of the center manifold can be found in Sec. III B.