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We consider cosmological dynamics in generalized modified gravity theory with the $R\Box R$ 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.
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