  A renormalized group improved Schwarzschild black hole spacetime contains two
quantum correction parameters. One parameter $\gamma$ represents the
identification of cutoff of the distance scale, and another parameter $\Omega$
stems from nonperturbative renormalization group theory. The two parameters are
constrained by the data from the shadow of M87* central black hole. The
dynamics of electrically charged test particles around the black hole are
integrable. However, when the black hole is immersed in an external
asymptotically uniform magnetic field, the dynamics are not integrable and may
allow for the occurrence of chaos. % English Editor: %Please verify that the
intended meaning has been retained. Employing an explicit symplectic
integrator, we survey the contributions of the two parameters to the chaotic
dynamical behavior. It is found that a small change of the parameter $\gamma$
constrained by the shadow of M87* black hole has an almost negligible effect on
the dynamical transition of particles from order to chaos. However, a small
decrease in the parameter $\Omega$ leads to an enhancement in the strength of
chaos from the global phase space structure. A theoretical interpretation is
given to the different contributions. The term with the parameter $\Omega$
dominates the term with the parameter $\gamma$, even if the two parameters have
same values. % English Editor: Please verify %that the intended meaning has
been retained. In particular, the parameter $\Omega$ acts as a repulsive force,
and its decrease means a weakening of the repulsive force or equivalently
enhancing the attractive force from the black hole. On the other hand, there is
a positive Lyapunov exponent that is universally given by the surface gravity
of the black hole when $\Omega\geq 0$ is small and the external magnetic field
vanishes.
