Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales

Volume 9, Issue 3, pp 1019--1034 http://dx.doi.org/10.22436/jnsa.009.03.30

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Authors

Yongkun Li - Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China. Pan Wang - Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China. Bing Li - Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China.

Abstract

In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the permanence of the system. Then we prove a Massera type theorem for impulsive dynamic equations on time scales and based on this theorem, we establish a criterion for the existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results. Our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new.

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Keywords

• Impulsive single-species model
• comparison theorem
• permanence
• almost periodic solution
• time scales.

MSC

•  34K12
•  34K14
•  34N05
•  92D25

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