Abstract: We studied the existence of positive periodic solution for a kind of predatorprey cubic Kolmogorov impulsive system. The system is transformed into equivalent operator equations by introducing operator in the suitable Banach space. By means of property of homotopy invariance of coincidence degree, it is proved that the operator satisfies the conditions of continuation theorem in coincidence degree. The sufficient conditions of the existence of positive periodic solution for the system are obtained. The paper generalizes and improves the result in the literature.

Key words: positive solution, impulsive differential equation, coincidence degree