  We discuss the intrinsic relations between thermodynamic phase transitions
and quasinormal modes in regular AdS black holes, specifically in the Bardeen
and Hayward AdS classes. To this end, we calculate the quasinormal modes of
massless scalar field perturbations around small and large black holes via the
Horowitz-Hubeny method. By investigating the isobaric and isothermal phase
transitions for Bardeen and Hayward AdS black holes in detail, we observe that
a dramatic change of quasinormal modes appears near the phase transition point
of small and large black holes, and that it corresponds to the swallow tail
structure in the plane of Gibbs free energy with respect to pressure. Moreover,
by analyzing the evolution of black holes along the coexistence curve of small
and large black hole phases, we also observe the dramatic change in quasinormal
modes. Such a phenomenon confirms the signal of the phase transition in the
quasinormal mode spectrum, which can be understood as a thermodynamic signal
hidden in the dynamical spectrum.
