  e provide a detailed analysis of a topological structure of a fermion
spectrum in the Hofstadter model with different hopping integrals along the
$x,y,z$-links ($t_x=t, t_y=t_z=1$), defined on a honeycomb lattice. We have
shown that the chiral gapless edge modes are described in the framework of the
generalized Kitaev chain formalism, which makes it possible to calculate the
Hall conductance of subbands for different filling and an arbitrary magnetic
flux $\phi$. At half-filling the gap in the center of the fermion spectrum
opens for $t>t_c=2^{\phi}$, a quantum phase transition in the 2D-topological
insulator state is realized at $t_c$. The phase state is characterized by zero
energy Majorana states localized at the boundaries. Taking into account the
on-site Coulomb repulsion $U$ (where $U<<1$), the criterion for the stability
of a topological insulator state is calculated at $t<<1$, $t \sim U$. Thus, in
the case of $ U > 4\Delta $, the topological insulator state, which is
determined by chiral gapless edge modes in the gap $\Delta$, is destroyed.
