We introduce a differential equation for star formation in galaxies that incorporates negative feedback with a delay .
When the feedback is instantaneous , solutions approach a self-limiting equilibrium state .
When there is a delay , even though the feedback is negative , the solutions can exhibit cyclic and episodic solutions .
We find that periodic or episodic star formation only occurs when two conditions are satisfied .
Firstly the delay timescale must exceed a cloud consumption timescale .
Secondly the feedback must be strong .
This statement is quantitatively equivalent to requiring that the timescale to approach equilibrium be greater than approximately twice the cloud consumption timescale .
The period of oscillations predicted is approximately 4 times the delay timescale .
The amplitude of the oscillations increases with both feedback strength and delay time .

We discuss applications of the delay differential equation ( DDE ) model to star formation in galaxies using the cloud density as a variable .
The DDE model is most applicable to systems that recycle gas and only slowly remove gas from the system .
We propose likely delay mechanisms based on the requirement that the delay time is related to the observationally estimated time between episodic events .
The proposed delay timescale accounting for episodic star formation in galaxy centers on periods similar to P \sim 10 Myrs , irregular galaxies with P \sim 100 Myrs , and the Milky Way disk with P \sim 2 Gyr , could be that for exciting turbulence following creation of massive stars , that for gas pushed into the halo to return and interact with the disk and that for spiral density wave evolution , respectively .