Barotropic index w-singularities in cosmology

We find an explicit cosmological model which allows a special type of cosmological singularity which we call a w-singularity. This singularity has the scale factor finite, the energy density and pressure vanishing, and the only singular behavior appears in a time-dependent barotropic index w(t). It is different from the type IV cosmological singularity in that it does not exhibit the divergence of the higher derivatives of the Hubble parameter and from the big brake since it does not fulfill the anti-Chaplygin gas equation of state. We also find an interesting duality between the w-singularities and the big-bang singularities. Physical examples of w-singularities appear in f(R), scalar field and brane cosmologies.