A pulsating star (pulsating variable star) is a variable star that varies because of pulses in its energy release, i.e., stellar pulsation. Layers of such a star expand and contract in an oscillation rather than settle into hydrostatic equilibrium. Among the specific types that fall under this class:
Long period variables (LPV), variable stars with periods of on the order of days, or hundreds, or thousands of days (various thresholds are used) are generally pulsating giant stars. Among them are Mira variables (a type of AGB star, type M in the General Catalogue of Variable Stars). The term slow irregular variable is something of a catch-all for types of stars with that description that are not yet comprehended.