  Using the FermiDirac distribution function, Balart and Vagenas gave a charged
spherically symmetric regular black hole, which is a solution of Einstein field
equations coupled to a nonlinear electrodynamics. In fact, the regular black
hole is a Reissner-Nordstrom (RN) black hole when a metric function is given a
Taylor expansion to first order approximations. It does not have a curvature
singularity at the origin,but the RN black hole does. Both black hole metrics
have horizons and similar asymptotic behaviors, and satisfy the weak energy
conditions everywhere. They are almost the same in photon effective potentials,
photon circular orbits and photon spheres outside the event horizons. There are
relatively minor differences between effective potentials, stable circular
orbits and innermost stable circular orbits of charged particles outside the
event horizons of the two black holes immersed in external magnetic fields.
Although the twomagnetized black holes allow different construction methods of
explicit symplectic integrators, they exhibit approximately consistent results
in the regular and chaotic dynamics of charged particles outside the event
horizons. Chaos gets strong as the magnetic field parameter or the magnitude of
negative Coulomb parameter increases, but becomes weak when the black hole
charge or the positive Coulomb parameter increases. A variation of dynamical
properties is not sensitive dependence on an appropriate increase of the black
hole charge. The basic equivalence between the two black hole gravitational
systems in the dynamics of orbits outside the event horizons is due to the two
metric functions having an extremely small difference. This implies that the RN
black hole is reasonably replaced by the regular black hole without curvature
singularity in many situations.
