  This work comes as the second part in a series of investigations into the
dynamics of rotating waves as solutions to lattice dynamical systems. Such
nonlinear waves as solutions to mathematical equations are of great interest
throughout the physical sciences due to their association with many
electrophysiological pathologies and this investigation aims to further the
understanding of rotating waves from a mathematical perspective. Here we focus
on so-called Lambda-Omega differential equations, a well-studied generalization
of the celebrated Ginzburg-Landau equation, to show that there exists an
interval of sufficiently small coupling values for which a rotating wave
solution persists. This result is achieved using a wide range of functional
analytic tools, primarily in an effort to apply a non-standard Implicit
Function Theorem. This work initiates subsequent studies into the dynamics and
bifurcations of rotating waves away from the reaction-diffusion equation
setting to differential equations for which traditional symmetry based centre
manifold reductions cannot be applied.
