Existence and stability of a unique almost periodic solution for a prey-predator system with impulsive effects and multiple delays

Advances in Difference Equations

Baodan Tian¹  Ning Chen²  Shouming Zhong² 

[1] Institute of Modeling and Algorithm, School of Science, Southwest University of Science and Technology, Mianyang, China;School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China

关键词: impulsive effects;    delays;    permanence;    almost periodic solution;    asymptotical stability;   

DOI  :  10.1186/s13662-016-0915-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, a nonautonomous almost periodic prey-predator system with impulsive effects and multiple delays is considered. By the mean-value theorem of multiple variables, integral inequalities, differential inequalities, and other mathematical analysis skills, sufficient conditions which guarantee the permanence of the system are obtained. Furthermore, by constructing a series of Lyapunov functionals, we derive that there exists a unique almost periodic solution of the system which is uniformly asymptotically stable. Finally, a numerical example and some simulations are presented to support our theoretical results.

【 授权许可】

CC BY