  In this note, we present a condition which guarantees spatial uniformity for
the asymptotic behavior of the solutions of a reaction-diffusion PDE with
Neumann boundary conditions in one dimension, using the Jacobian matrix of the
reaction term and the first Dirichlet eigenvalue of the Laplacian operator on
the given spatial domain. We also derive an analog of this PDE result for the
synchronization of a network of identical ODE models coupled by diffusion
terms.
