  In this manuscript we consider the stability of periodic solutions to
Lambda-Omega lattice dynamical systems. In particular, we show that an
appropriate ansatz casts the lattice dynamical system as an
infinite-dimensional fast-slow differential equation. In a neighbourhood of the
periodic solution an invariant slow manifold is proven to exist, and that this
slow manifold is uniformly exponentially attracting. The dynamics of solutions
on the slow manifold become significantly more complicated and require a more
delicate treatment. We present sufficient conditions to guarantee convergence
on the slow manifold which is algebraic, as opposed to exponential, in the
slow-time variable. Of particular interest to our work in this manuscript is
the stability of a rotating wave solution, recently found to exist in the
Lambda-Omega systems studied herein.
