Phantom-like GCG and the constraints of its parameters via cosmological dynamics

We extend the equation of state of GCG (Generalized Chaplygin Gas) to $w<-1$ regime and show, from the point of view of dynamics, that the parameters of GCG should be in the range of $0<\alpha <1$. Also, dynamical analysis indicate that the phase $w_g=-1$ is a dynamical attractor and the equation of state of GCG approaches it from either $w_g>-1$ or $w_g<-1$ depending on the choice of its initial cosmic density parameter and the ratio of pressure to critical energy density.