  We investigate the stability of both timelike as well as null circular
geodesics in the vicinity of a dual (3+1) dimensional stringy black hole (BH)
spacetime by using an excellent tool so-called Lyapunov exponent. The proper
time ($\tau$) Lyapunov exponent ($\lambda_{p}$) and coordinate time ($t$)
Lyapunov exponent~($\lambda_{c}$) are explicitly derived to analyze the
stability of equatorial circular geodesics for the stringy BH spacetime with
\emph{electric charge} parameter ($\alpha$) and \emph{magnetic charge}
parameter~($Q$). By computing these exponents for both the cases of BH
spacetime, it is observed that the coordinate time Lyapunov exponent of
magnetically charged stringy BH for both timelike and null geodesics are
independent of magnetic charge parameter $(Q)$. The variation of the ratio of
Lyapunov exponents with radius of timelike circular orbits ($r_{0}/M$) for both
the cases of stringy BH are presented. The behavior of instability exponent for
null circular geodesics with respect to charge parameters ($\alpha$ and $Q$)
are also observed for both the cases of BH. Further, by establishing a relation
between quasinormal modes (QNMs) and parameters related to null circular
geodesics (like angular frequency and Lyapunov exponent), we deduced the QNMs
(or QNM frequencies) for a massless scalar field perturbation around
\emph{both} the cases of stringy BH spacetime in the eikonal limit. The
variation of scalar field potential with charge parameters and angular momentum
of perturbation ($l$) are visually presented and discussed accordingly.
