  In this study, we explore the dynamical stability of magnetar bursts within
the context of the chaos-randomness phase space for the first time, aiming to
uncover unique behaviors compared to various astrophysical transients,
including fast radio bursts (FRBs). We analyze burst energy time series data
from active magnetar sources SGR J1550-5418 and SGR J1935+2154, focusing on
burst arrival time and energy differences between consecutive events. We find a
distinct separation in the time domain, where magnetar bursts exhibit
significantly lower randomness compared to FRBs, solar flares, and earthquakes,
with a slightly higher degree of chaos. In the energy domain, magnetar bursts
exhibit a broad consistency with other phenomena, primarily due to the wide
distribution of chaos-randomness observed across different bursts and sources.
Intriguingly, contrary to expectations from the FRB-magnetar connection, the
arrival time patterns of magnetar bursts in our analysis do not exhibit
significant proximity to repeating FRBs in the chaos-randomness plane. This
finding may challenge the hypothesis that FRBs are associated with typical
magnetar bursts but indirectly supports the evidence that FRBs may primarily be
linked to special magnetar bursts like peculiar X-ray bursts from SGR
J1935+2154 observed simultaneously with Galactic FRB 200428.
