  We study spin-wave excitations in a circular ferromagnetic nanodot in
different inhomogeneous, topologically non-trivial magnetization states,
specifically, vortex and skyrmion states. Gradual change in the strength of the
out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange
interaction leads to continuous phase transitions between different stable
magnetic configurations and allows for mapping of dynamic spin modes in and
between the vortex, Bloch-type skyrmion and N\'eel-type skyrmion states. Our
study elucidates the connections between gyrotropic modes, azimuthal spin waves
and breathing modes in various stable magnetization states and helps to
understand the rich spin excitation spectrum on the skyrmion background.
