# QUALITATIVE ANALYSIS OF A GENERAL PERIODIC SYSTEM

• Xu, Shihe (School of Mathematics and Statistics Zhaoqing University)
• Accepted : 2017.09.28
• Published : 2018.07.31

#### 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.

#### Acknowledgement

Supported by : NSF of China, Foundation for Outstanding Young Teachers in Higher Education of Guangdong

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