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The dark energy model with the equation of state p_d=-rho_d - A rho_d^alphais studied. The model comprises and provides realization of several types ofsingularities in different parameter regimes: the divergence of the dark energydensity and pressure at finite time and finite value of the scale factor, thesingularity of the "big rip" type and the sudden future singularity recentlyintroduced by Barrow. For parameter choices which lead to a nonsingularexpansion of the universe, various types of the asymptotic evolution are found.The entire time evolution of the universe is described both analytically andnumerically. The advantages of this dark energy EOS as a parametrization ofdark energy are discussed.Comment: v1: 8 pages, 8 figures. v2: references added. v3: discussions and  references added. Version to appear in Phys. Rev.

Expansion around the vacuum equation of state: Sudden future singularities and asymptotic behavior