  In this work we study the autonomous dynamical system of different $F(R)$
models in the formalism of holographic dark energy using the generalized
Nojiri-Odintsov cut-off. We explicitly give the expression of the fixed points
as functions of the infrared cut-off for vacuum $F(R)$ gravity in flat and
non-flat FRW background and for $F(R)$ coupling axion dark matter. Each fixed
point component can be taken as a condition on the cut-off and on the
expression of $F(R)$, leading to physically interesting constraints on these
functions.
