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We investigate the stability of both timelike as well as null circulargeodesics in the vicinity of a dual (3+1) dimensional stringy black hole (BH)spacetime by using an excellent tool so-called Lyapunov exponent. The propertime ($\tau$) Lyapunov exponent ($\lambda_{p}$) and coordinate time ($t$)Lyapunov exponent~($\lambda_{c}$) are explicitly derived to analyze thestability 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 BHspacetime, it is observed that the coordinate time Lyapunov exponent ofmagnetically charged stringy BH for both timelike and null geodesics areindependent of magnetic charge parameter $(Q)$. The variation of the ratio ofLyapunov exponents with radius of timelike circular orbits ($r_{0}/M$) for boththe cases of stringy BH are presented. The behavior of instability exponent fornull circular geodesics with respect to charge parameters ($\alpha$ and $Q$)are also observed for both the cases of BH. Further, by establishing a relationbetween quasinormal modes (QNMs) and parameters related to null circulargeodesics (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. Thevariation of scalar field potential with charge parameters and angular momentumof perturbation ($l$) are visually presented and discussed accordingly.

Stability Analysis of Geodesics and Quasinormal Modes of a Dual Stringy Black Hole Via Lyapunov Exponents