  In this paper, employing the modified dispersion relation, we have derived
the general modified Friedmann equations and the corresponding modified entropy
relations for the Friedmann-Robertson-Walker (FRW) Universe. In this setup, we
find that when the big bounce happens, its energy scale and its corresponding
modified entropy behavior are sensitive to the value of $k$. In contrast to the
previous work with $k=0$, our work mainly demonstrates that the bouncing
behavior for the closed Universe with $k=1$ appears at the normal energy limit
of the modified dispersion relation introduced, and when bouncing phenomenon is
in presence, its modified entropy is just equal to zero. Surprisingly, when
$k=-1$, the bouncing behavior is in absence.
