Long-time behavior of Ginzburg-Landau systems far from equilibrium

Using singular-perturbation techniques, we study the stability of modulated structures generated by driving Ginzburg-Landau systems far from equilibrium. We show that, far from equilibrium, the steady-state behavior is controlled by an effective Lagrangian which possesses the same functional form as the original free energy but with renormalized coefficients. We study both linear and nonlinear sources and determine their influence on the long-term stability of the bifurcating solutions