Before revision:  Despite the complicated dynamics, we are able to aptly identify a region in the parameter space where the dynamics manifests universal and robust features which extend to the weakly non-linear regime. Large scale variations of patterns are well captured by a Ginzburg-Landau equation , whose form does not depend on the details of the underlying models.
After revision:  Despite the complicated dynamics, we are able to aptly identify a region in the parameter space where the dynamics manifests universal and robust features which extend to the details of the dynamics. Hence, we demonstrate the validity of such equation in the description of the behavior of a wide class of systems. We introduce a novel mathematical framework that is also able to retrieve the analytical expressions of the coefficients appearing in the Ginzburg-Landau equation , whose form does not depend on the details of the underlying models.