  Rotating waves are a fascinating feature of a wide array of complex systems,
particularly those arising in the study of many chemical and biological
processes. With many rigorous mathematical investigations of rotating waves
relying on the model exhibiting a continuous Euclidean symmetry, this work is
aimed at understanding these nonlinear waves in the absence of such symmetries.
Here we will consider a spatially discrete lattice dynamical system of
Ginzburg-Landau type and prove the existence of rotating waves in the
anti-continuum limit. This result is achieved by providing a link between the
work on phase systems stemming from the study of identically coupled
oscillators on finite lattices to carefully track the solutions as the size of
the lattice grows. It is shown that in the infinite square lattice limit of
these phase systems that a rotating wave solution exists, which can be extended
to the Ginzburg-Landau system of study here. The results of this work provide a
necessary first step in the investigation of rotating waves as solutions to
lattice dynamical systems in an effort to understand the dynamics of such
solutions outside of the idealized situation where the underlying symmetry of a
differential equation can be exploited.
