  Eigen's quasispecies system with explicit space and global regulation is
considered. Limit behavior and stability of the system in a functional space
under perturbations of a diffusion matrix with nonnegative spectrum are
investigated. It is proven that if the diffusion matrix has only positive
eigenvalues then the solutions of the distributed system converge to the
equilibrium solution of the corresponding local dynamical system. These results
imply that the error threshold does not change if the spatial interactions
under the principle of global regulation are taken into account.
