On the Kneser property for the complex Ginzburg–Landau equation and the Lotka–Volterra system with diffusion

We study the Kneser property (i.e. the compactness and connectedness for the attainability set of solutions) for a reaction–diffusion system including as a particular case the complex Ginzburg–Landau equation and the Lotka–Volterra system with diffusion. Using this property we obtain also that the global attractor of this system in both the autonomous and non-autonomous cases is connected.