Dark energy cosmology with generalized linear equation of state

We describe the cosmology of a perfect fluid with a linear equation of state of a general form p=\α(\ρ-\ρ_0), where the constants \α and \ρ_0 are free parameters. This model comprises as the the particular cases the standard cosmological scenarios with the domination of radiation, w=p/\ρ=1/3, or cold dark matter, $p=0$, and the new ones in the form of a dark energy with the relativistic negative pressure w<-1/3. The possible types of cosmological scenarios in this model are determined and classified in terms of attractors and unstable points by the using of phase trajectories analysis. For a dark energy case there are possible some distinctive types of cosmological scenarios: (i) the universe with the de Sitter attractor at late times, (ii) the bouncing universe, (iii) the universe with the Big Rip and with the anti-Big Rip. In the framework of a linear equation of state the universe filled with a phantom energy, w<-1, may have either the de Sitter attractor or the Big Rip.