Attractor solutions for general hessence dark energy

As a candidate for the dark energy, the hessence model has been recently introduced. We discuss the critical points of this model in an almost general case, that is for arbitrary hessence potential and almost arbitrary hessence-background matter interaction. It is shown that, in all models, there always exist some stable late-time attractors. It is shown that our general results coincide with those solutions obtained earlier for special cases, but some of them are new. These new solutions have two unique characteristics. First, the hessence field has finite value in these solutions and, second, their stabilities depend on the second derivative of the hessence potential.