We consider a star 'dies' once all the burnable H (via nuclear fusion) in the interior of a star is depleted. Stars that are more massive than roughly 8 times the Sun throw out a large chunk of its mass in the form of an explosion. We call it a 'supernova'. This large chunk of mass can have velocities close to 3000-5000 km/s. This high-velocity ejecta from a supernova can push gas out to make a gaseous 'hole' in the galaxy and heat the surrounding material so that gas can not condense and form stars. One of my interests is the evolution of the supernova remnant and its interaction with the surrounding material (or the interstellar medium, ISM). 

Bubbles (gaseous holes) created by supernovae make the ISM porous. With high porosity, star formation declines and vice versa. With lower star formation, there are a lower number of stars that go off as supernovae which in turn reduces the number of bubbles and, therefore, increases the star formation. Each of these processes takes a certain time to make an impact on the ISM. Therefore, the ISM goes back and forth in star formation and supernova rates. After a certain number of such going back and forth, the ISM comes to an equilibrium where the creation and destruction of these bubbles become equal. At this point, the star formation also becomes steady and follows the famous star formation- gas density relation, also known as the Kennicutt-Schmidt relation of star formation.