  Meta-stable states are identified in the Ising model with competition between
the Glauber and Kawasaki dynamics. The model of interaction between magnetic
moments was implemented on a network where the degree distribution follows a
power-law of the form, $P(k)\sim k^{-\alpha}$. The evolution towards the
stationary state occurred through the competition between two dynamics, driving
the system out of equilibrium. In this competition, with probability $q$, the
system was simulated in contact with a heat bath at temperature $T$ by the
Glauber dynamics, while with probability $1-q$, the system experienced an
external energy influx governed by the Kawasaki dynamics. The phase diagrams of
$T$ versus $q$ were obtained, which are dependent on the initial state of the
system, and exhibit first- and second-order phase transitions. In all diagrams,
for intermediate values of $T$, the phenomenon of self-organization between the
ordered phases was observed. In the regions of second-order phase transitions,
we have verified the universality class of the system through the critical
exponents of the order parameter $\beta$, susceptibility $\gamma$, and
correlation length $\nu$. Furthermore, in the regions of first-order phase
transitions, we have demonstrated the instability due to transitions between
the ordered phases through hysteresis-like curves of the order parameter, in
addition to the existence of absorbing states. We also estimated the value of
the tricritical points when the discontinuity in the order parameter in the
phase transitions was no longer observed.
