Title: A Study on the Stability Analysis of Mathematical Model leading to the Star Formation

Abstract It takes millions of years for a star to get formed. This paper deals with the stability analysis of mathematical model which governs star formation. Variation matrix or Jacobian Matrix is developed out of differential equation which arises from three component of galactic region i.e. atomic, molecular and stellar components. Mathematical Model is the best way to explore and explain the system of three components in the galactic region. In fact, Mathematical Modelling- is the main, if not the only way one, way for theoretical research of astrophysical processes and objects [6]. Various examples has been taken for comparative studies and computational purposes Keywords: Galactic region, interstellar medium, giant molecular mass, stellar evolution, galaxy, star formation.