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Motivated by the recent observations for the cosmic acceleration and thesuitable evolution of the Universe provided an interaction (decay of darkenergy to matter) is incorporated in a cosmological model, we study thecosmological evolution of the Interacting Holographic Dark Energy scenario.Critical points are derived and their corresponding cosmological models arepresented. The dynamical character of these models is revealed.

The Cosmological Dynamics of Interacting Holographic Dark Energy Model