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August  2004, 4(3): 555-562. doi: 10.3934/dcdsb.2004.4.555

A monotone-iterative method for finding periodic solutions of an impulsive competition system on tumor-normal cell interaction

Jiawei Dou 1, , Lan-sun Chen 2, and  Kaitai Li 3,

1. 

College of Mathematics and Information Science, Shanxi Normal University, Xi'an 710062, China
2. 

Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, China
3. 

Research Center for Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049, China

Received  October 2002 Revised  August 2003 Published  May 2004

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: competition system, Impulsive, tumor-normal cell interaction., monotone-iterative method, periodic solution.
Mathematics Subject Classification: 34A37, 92D2.
Citation: Jiawei Dou, Lan-sun Chen, Kaitai Li. A monotone-iterative method for finding periodic solutions of an impulsive competition system on tumor-normal cell interaction. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 555-562. doi: 10.3934/dcdsb.2004.4.555
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