A monotone-iterative method for finding periodic solutions of an impulsive competition system on tumor-normal cell interaction
Open Access
- 1 January 2004
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems-Series B
- Vol. 4 (3) , 555-562
- https://doi.org/10.3934/dcdsb.2004.4.555
Abstract
In this paper, a monotone-iterative scheme is established for finding positive periodic solutions of a competition model of tumor-normal cell interaction. The model describes the evolution of a population with normal and tumor cells in a periodically changing environment. This population is under periodical chemotherapeutic treatment. Competition among the two kinds of cells is considered. The mathematical problem involves a coupled system of Lotka-Volterra together with periodically pulsed conditions. The existence of positive periodic solutions is proved by the monotone iterative technique and in a special case, the uniqueness of a periodic solution is obtained by proving that any two periodic solutions have the same average. Moreover, we also show that the system is permanent under the conditions which guarantee the existence of the periodic solution. Some computer simulations are carried out to demonstrate the main results.Keywords
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