Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2018; 33(3): 1039-1048

Online first article March 20, 2018      Printed July 1, 2018

https://doi.org/10.4134/CKMS.c170267

Copyright © The Korean Mathematical Society.

Qualitative analysis of a general periodic system

Shihe Xu

Zhaoqing University

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

MSC numbers: 34C25, 34D05