  In this paper, we investigate influences of the charge and angular momentum
of a particle around a charged Einstein-Euler-Heisenberg AdS black hole on a
Lyapunov exponent, and find spatial regions where the chaos bound is violated.
Positions of circular orbits are gotten by fixing the charge and angular
momentum of the particle, respectively. The positions gradually move away from
the event horizon with the increase of the angular momentum when the charge is
fixed and with the decrease of the charge when the angular momentum is fixed.
For certain values of the charge, angular momentum and Euler-Heisenberg
parameter, the spatial regions where the bound is violated are found. When the
charge is fixed and the Euler-Heisenberg parameter is large, a small angular
momentum causes the violation. Although the angular momentum is small, the
corresponding spatial region is not small. An interesting discovery is that the
bound is violated by the black hole when the particle's charge is less than 1
and $\Lambda =0$, but this requires the black hole's charge to be large enough.
This violation may be related to the dynamical stability of the black hole. The
backreaction of the particle on the background spacetime isn't considered in
the investigation.
