The Periodic Solutions of Impulsive Competition System on Tumor-Normal Cell Interaction

Abstract

In this work we investigate a problem of existence of positive periodic solutions for a class of impulsive differential equations in the plane. This describes generally the competition between normal and tumor cells in a periodically changing environment under chemotherapeutic treatment. The mathematical problem involves a coupled system of Lotka-Volterra together with periodically pulsed conditions. We use the monotone method to construct the upper and lower sequences converging to the periodic solution of the system.