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.

2008 ◽  
Vol 14 (1) ◽  
pp. 59-81 ◽  
Author(s):  
Yonghui Xia ◽  
Sui Sun Cheng
Keyword(s):  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Population Dynamic ◽  
Natural Science ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Education Commission ◽  
Uniformly Asymptotic Stability

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

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Heping Ma ◽  
Jianguo Gao ◽  
Lingling Xie
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Competitive Model ◽  
Uniformly Asymptotic Stability ◽  
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.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Qinglong Wang ◽  
Zhijun Liu
Keyword(s):  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Competitive System ◽  
Analysis Techniques ◽  
Uniformly Asymptotic Stability ◽  
Positive Almost Periodic Solution ◽  
Positive Almost Periodic Solutions

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.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Wenshuang Yin
Keyword(s):  
Feedback Control ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Discrete System ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Uniformly Asymptotic Stability ◽  
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.

scholarly journals Existence and Global Uniform Asymptotic Stability of Pseudo Almost Periodic Solutions for Cohen-Grossberg Neural Networks with Discrete and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hongying Zhu ◽  
Chunhua Feng
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Distributed Delays ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniform Asymptotic Stability ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

This paper studies the existence and uniform asymptotic stability of pseudo almost periodic solutions to Cohen-Grossberg neural networks (CGNNs) with discrete and distributed delays by applying Schauder fixed point theorem and constructing a suitable Lyapunov functional. An example is given to show the effectiveness of the main results.

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