  We study the dynamical stability of hairy dyonic black holes in the
Einstein-Maxwell-scalar gravity system against the massless scalar field
perturbation. We numerically obtain the corresponding quasinormal modes (QNMs)
using the series solution and shooting methods for various black hole
parameters. We find that the numerical values obtained from these two methods
agree well with each other. The imaginary part of the QNM is always negative,
indicating the stability of the dyonic hairy black hole against the scalar
perturbation. We find that the decay and oscillatory modes of the scalar field
perturbation increase linearly with the horizon radius for large black holes.
We thoroughly investigate the behaviour of QNMs for different values of black
hole parameters, including the electric charge, magnetic charge, horizon radius
and hairy parameter, etc. Moreover, we also analyse the QNM near the
small/large black hole phase transition and find that the nature of the QNMs is
different for large and small black hole phases, suggesting QNMs as the
possible probe of black hole phase transition.

General Relativity and Quantum Cosmology;High Energy Physics - Theory