Technically, collapsing of a star as a whole at any point of time happens dynamically, but due to the thermal timescale being much higher, the compression can be considered nearly adiabatic, which causes the star to become hotter and brighter and maintains hydrostatic equilibrium at a dynamical timescale. (There is little involvement of the core here since the photon diffusion timescales are high - ~ 100,000 years - and any effect of the core on the star will be seen much much later.) This is why you never see a 'star' collapse. You can, at best, see them pulsate. Typically the core is what collapses, which alters fusion rates and hence is NOT adiabatic. I will try to explain this process in a little detail; let me know if that answers you question.
When the star is almost out of fuel, it cannot burn fuel as effectively as before, so, the core compresses a little, increasing the temperature, which increases the efficiency and rate of fusion, which makes the 'running out of fuel' part faster leading to a positive feedback process (compression $\rightarrow$ faster exhaustion $\rightarrow$ more compression). This gradually keeps 'collapsing' and burning fuel faster till a point where it cannot counter the collapse using an increased fusion rate due to lack of sufficient fuel (this might still take a few million years, maybe, but it keeps collapsing faster in a runaway fashion till that point). Beyond this point, the collapse happens at the dynamical timescale till it hits degeneracy (or ignition temperature of the previously inert core), which leads to puffing, novae and supernovae based on the mass of the core and its composition.