This paper investigates the proposed oscillatory model of a star formation system, including in-fall of gas from the local environment and outflow of gas due to supernovae explosions and other perturbations. In particular, the objective is to study how the variable density of the interstellar components- atomic, molecular, and stellar interact with the star formation cycle. The oscillatory nature of the model is observed due to the modeling of fractional masses of the components. The model exhibited characteristics of both unimodal and episodes of decreasing amplitude of star formation, being both dynamically open and closed. Under different special parametric conditions, both limit cycle and stationary state behavior are observed. This indicates the existence of a stable star formation cycle in discrete episodes and an unstable star formation cycle converging to a definite point. Observations of duty cycles under various parameters with varying intensity of supernovae for dwarf galaxies showed the star formation system adopts a self-regulatory oscillatory state beyond a particular value. However, a similar analysis for giant galaxies showed the oscillatory period to decrease over a period of time for higher values. This may be implied by the low production rate of the supernova in dwarf galaxies, increasing the production of cold gas, continuing the cycle for a longer time.