  We study a coupled nonlinear evolution system arising from the
Ginzburg-Landau theory for atomic Fermi gases near the BCS-BEC crossover.
First, we prove that the initial boundary value problem generates a strongly
continuous semigroup on a suitable phase-space which possesses the global
attractor. Then we establish the existence of an exponential attractor. As a
consequence, we show that the global attractor is of finite fractal dimension.
