Cosmological Evolution of Hessence Dark Energy and Avoidance of Big Rip

Recently, many dark energy models whose equation-of-state parameter can cross the phantom divide $w_{de}=-1$ have been proposed. In a previous paper [Class. Quant. Grav. {\bf 22}, 3189 (2005); hep-th/0501160], we suggest such a model named hessence, in which a non-canonical complex scalar field plays the role of dark energy. In this work, the cosmological evolution of the hessence dark energy is investigated. We consider two cases: one is the hessnece field with an exponential potential, and the other is with a (inverse) power law potential. We separately investigate the dynamical system with four different interaction forms between hessence and background perfect fluid. It is found that the big rip always does not appear in the hessence model even in the most general case beyond above particular potentials and interaction forms.