Cosmological dynamics in six-order gravity

We consider cosmological dynamics in generalized modified gravity theory with the $R\mathrm{\square }R$ term added to the action of the form $R+R^N$. Influence of $R \Box R$ term to the known solutions of modified gravity is described. We show that in particular case of $N=3$ these two non-Einstein terms are equally important on power-law solutions. These solutions and their stability have been studied using dynamical system approach. Some results for the case of $N\mathrm{\ne }3$ (including stability of de Sitter solution in the theory under investigation) have been found using other methods.