One way to reduce the dimension of a system of equations is through the use of deterministic center manifold theory. In general, a nonlinear vector field can be transformed so that the linear part ͑Jacobian͒ of the vector field has a block diagonal form where the first matrix block has eigenvalues with positive real part, the second matrix block has eigenvalues with negative real part, and the third matrix block has eigenvalues with zero real part. 30, 31 These blocks are associated, respectively, with the unstable eigenspace, the stable eigenspace, and the center eigenspace. If we suppose that there are no eigenvalues with positive real part, then orbits will rapidly decay to the center eigenspace.