Stability analysis of the Tsallis holographic dark energy model

Using the generalized Tsallis entropy, the Tsallis holographic dark energy(THDE) was proposed recently. In this paper we analyze the cosmological consequences of the THDE model with an interaction between dark energy and dark matter $Q=H(\alpha {\rho }_m+\beta {\rho }_D)$. We find that the THDE model can explain the current accelerated cosmic expansion, and it is stable under certain conditions. Furthermore, through investigating the dynamical analysis, we find that there exists an attractor which represents an accelerated expansion phase of the universe. When $\beta =0$, this attractor corresponds to a dark energy dominated de Sitter solution and the universe can evolve into an era which is depicted by the $\mathrm{\Lambda }$CDM model. The age of universe in this model is also explored.