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http://dx.doi.org/10.4134/CKMS.c170267

QUALITATIVE ANALYSIS OF A GENERAL PERIODIC SYSTEM  

Xu, Shihe (School of Mathematics and Statistics Zhaoqing University)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.3, 2018 , pp. 1039-1048 More about this Journal
Abstract
In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.
Keywords
stability; periodic solution; mathematical model;
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1 M. Bai and S. Xu, Qualitative analysis of a mathematical model for tumor growth with a periodic supply of external nutrients, Pac. J. Appl. Math. 5 (2013), no. 4, 217-223.
2 S. Cui and S. Xu, Analysis of mathematical models for the growth of tumors with time delays in cell proliferation, J. Math. Anal. Appl. 336 (2007), no. 1, 523-541.   DOI
3 U. Forys, M. Bodnar, and Y. Kogan, Asymptotic dynamics of some t-periodic one- dimensional model with application to prostate cancer immunotherapy, J. Math. Biol. 73 (2016), no. 4, 867-883.   DOI
4 A. Friedman and F. Reitich, Analysis of a mathematical model for the growth of tumors, J. Math. Biol. 38 (1999), no. 3, 262-284.   DOI
5 J. C. Panetta, Mathematical models of chemotherapy, ProQuest LLC, Ann Arbor, MI, 1995.
6 J. Teixeira and M. J. Borges, Existence of periodic solutions of ordinary differential equations, J. Math. Anal. Appl. 385 (2012), no. 1, 414-422.   DOI