We model the star formation history ( SFH ) and the chemical evolution of the Galactic disk by combining an infall model and a limit-cycle model of the interstellar medium ( ISM ) .
Recent observations have shown that the SFH of the Galactic disk violently variates or oscillates .
We model the oscillatory SFH based on the limit-cycle behavior of the fractional masses of three components of the ISM .
The observed period of the oscillation ( \sim 1 Gyr ) is reproduced within the natural parameter range .
This means that we can interpret the oscillatory SFH as the limit-cycle behavior of the ISM .
We then test the chemical evolution of stars and gas in the framework of the limit-cycle model , since the oscillatory behavior of the SFH may cause an oscillatory evolution of the metallicity .
We find however that the oscillatory behavior of metallicity is not prominent because the metallicity reflects the past integrated SFH .
This indicates that the metallicity can not be used to distinguish an oscillatory SFH from one without oscillations .