  In this paper, we investigate thermodynamical structure of dyonic black holes
in the presence of gravity's rainbow. We confirm that for super magnetized and
highly pressurized scenarios, the number of black holes' phases is reduced to a
single phase. In addition, due to specific coupling of rainbow functions, it is
possible to track the effects of temporal and spatial parts of our setup on
thermodynamical quantities/behaviors including equilibrium point, existence of
multiple phases, possible phase transitions and conditions for having a uniform
stable structure.
