Phase space analysis of Tsallis agegraphic dark energy

Based on the generalized Tsallis entropy and holographic hypothesis, the Tsallis agegraphic dark energy (TADE) was proposed by introducing the timescale as infrared cutoff. In this paper, we analyze the evolution of the universe in the TADE model and the new Tsallis agegraphic dark energy (NTADE) model by considering an interaction between dark matter and dark energy as $$Q=H(\alpha \rho _{m}+\beta \rho _{D})$$ . Through the phase space and stability analysis, we find an attractor which represents a late-time accelerated expansion phase can exist only in NTADE model. When $$0\le \alpha <1$$ and $$\beta =0$$ , this attractor becomes a dark energy dominated de Sitter solution and the universe can eventually evolve into an accelerated expansion era which is depicted by the $$\Lambda $$ cold dark matter model. Thus, the expansion history of the universe can be depicted by the NTADE model.