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The model of generalized Tsallis holographic dark energy (which is known tobe particular representative of Nojiri-Odintsov HDE) with event horizon ascut-off is investigated using methods of dynamical analysis. We take intoconsideration possible interaction with dark energy and matter in variousforms. Critical points are determined. Cosmological evolution of the Universedepends from interaction parameters. If we use event horizon scale as cutoffquasi-de Sitter expansion is possible only for interaction of type $\simH(\alpha\rho_{de}+\beta\rho_{m})$ (where $H$ is the Hubble parameter). Forinteractions $\sim \rho_m \rho_{de} /H$ and $\sim H\rho_{m}^{\alpha}\rho_{de}^{1-\alpha}$ Universe eventually stops ($H\rightarrow0$) or ends its existence in final singularity ($H\rightarrow\infty$). In firstcase fraction of dark energy tends to $1$ or constant value lesser than 1because dynamical equilibrium between matter and dark energy is established onlate times.

Dynamical analysis of the Tsallis holographic dark energy models with event horizon as cut-off and interaction with matter