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 cannot be used to distinguish an oscillatory SFH from one without oscillations.
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