Abstract: This paper derived the necessary and sufficient condition for the existence of invariant real irreducible algebraic curve of a polynomial differential system. Using this result and quadratic polynomials of quadratic system, we established some criteria to determine whether equilibrium was circled by a closed orbit. Finally, a property of the equilibrium enclosed in a periodic orbit
was deduced for quadratic system.

Key words: invariant algebraic curve, quadratic differential system, periodic orbit, irreducible Darboux polynomial, invariant algebraic curve, quadratic differential system, periodic orbit