Feedback Control in a General Almost Periodic Discrete System of Plankton Allelopathy

Almost Periodic ◽

Feedback Controls ◽

Plankton Allelopathy

We study the properties of almost periodic solutions for a general discrete system of plankton allelopathy with feedback controls and establish a theorem on the uniformly asymptotic stability of almost periodic solutions.

Uniformly asymptotic stability of almost periodic solutions for a delay difference system of plankton allelopathy

Advances in Difference Equations ◽

10.1186/1687-1847-2013-283 ◽

2013 ◽

Vol 2013 (1) ◽

Cited By ~ 2

Author(s):

Qinglong Wang ◽

Zhijun Liu

Keyword(s):

Asymptotic Stability ◽

Periodic Solutions ◽

Difference System ◽

Almost Periodic ◽

Plankton Allelopathy ◽

Delay Difference ◽

Delay Difference System

Uniformly asymptotic stability of almost periodic solutions for a competitive system with impulsive perturbations

Advances in Difference Equations ◽

10.1186/1687-1847-2014-2 ◽

2014 ◽

Vol 2014 (1) ◽

pp. 2 ◽

Cited By ~ 3

Author(s):

Ronghua Tan ◽

Weifang Liu ◽

Qinglong Wang ◽

Zhijun Liu

Keyword(s):

Asymptotic Stability ◽

Periodic Solutions ◽

Almost Periodic ◽

Competitive System ◽

Impulsive Perturbations

Global Stability of Positive Periodic Solutions and Almost Periodic Solutions for a Discrete Competitive System

Discrete Dynamics in Nature and Society ◽

10.1155/2015/658758 ◽

2015 ◽

Vol 2015 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Heping Ma ◽

Jianguo Gao ◽

Lingling Xie

Keyword(s):

Asymptotic Stability ◽

Lyapunov Function ◽

Periodic Solutions ◽

Almost Periodic ◽

Positive Periodic Solutions ◽

Competitive System ◽

Competitive Model ◽

Positive Almost Periodic Solutions

A discrete two-species competitive model is investigated. By using some preliminary lemmas and constructing a Lyapunov function, the existence and uniformly asymptotic stability of positive almost periodic solutions of the system are derived. In addition, an example and numerical simulations are presented to illustrate and substantiate the results of this paper.

Quasi-uniformly asymptotic stability and existence of almost periodic solutions of difference equations with applications in population dynamic systemsThis work was supported by the National natural science foundation of China under grant (No.10671127) and Shanghai outstanding discipline leader project (No. 06XD14034) and Shanghai municipal education commission No. 06DZ002.

The Journal of Difference Equations and Applications ◽

10.1080/10236190701470407 ◽

2008 ◽

Vol 14 (1) ◽

pp. 59-81 ◽

Cited By ~ 12

Author(s):

Yonghui Xia ◽

Sui Sun Cheng

Keyword(s):

Asymptotic Stability ◽

Periodic Solutions ◽

Difference Equations ◽

Population Dynamic ◽

Natural Science ◽

Almost Periodic ◽

Education Commission ◽

Uniformly Asymptotic Stability

Uniformly Asymptotic Stability of Positive Almost Periodic Solutions for a Discrete Competitive System

Journal of Applied Mathematics ◽

10.1155/2013/182158 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 6

Author(s):

Qinglong Wang ◽

Zhijun Liu

Keyword(s):

Asymptotic Stability ◽

Periodic Solutions ◽

Almost Periodic Solution ◽

Almost Periodic ◽

Competitive System ◽

Analysis Techniques ◽

Positive Almost Periodic Solutions

Positive Almost Periodic Solution ◽

This paper is devoted to the study of almost periodic solutions of a discrete two-species competitive system. With the help of the methods of the Lyapunov function, some analysis techniques, and preliminary lemmas, we establish a criterion for the existence, uniqueness, and uniformly asymptotic stability of positive almost periodic solution of the system. Numerical simulations are presented to illustrate the analytical results.