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

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Qinglong Wang ◽  
Zhijun Liu
Keyword(s):  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Difference System ◽  
Almost Periodic ◽  
Uniformly Asymptotic Stability ◽  
Plankton Allelopathy ◽  
Delay Difference ◽  
Delay Difference System

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 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.

ASYMPTOTIC STABILITY OF NONLINEAR DELAY-DIFFERENCE SYSTEM VIA MATRIX INEQUALITIES AND APPLICATION

2009 ◽  
Vol 06 (03) ◽  
pp. 389-397 ◽  
Author(s):  
K. RATCHAGIT
Keyword(s):  
Asymptotic Stability ◽  
Zero Solution ◽  
Discrete Version ◽  
Multiple Delays ◽  
Difference System ◽  
Matrix Inequalities ◽  
Delay Difference ◽  
Lyapunov Second Method ◽  
Nonlinear Delay ◽  
Delay Difference System

In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference system of nonlinear delay-difference system in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result is applied to obtain new stability condition in terms of certain matrix inequalities for some class of nonlinear delay-difference system such as delay-difference system of nonlinear delay-difference system with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational purposes.

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.

ASYMPTOTIC STABILITY OF DELAY-DIFFERENCE SYSTEM OF HOPFIELD NEURAL NETWORKS VIA MATRIX INEQUALITIES AND APPLICATION

2007 ◽  
Vol 17 (05) ◽  
pp. 425-430 ◽  
Author(s):  
KREANGKRI RATCHAGIT
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Zero Solution ◽  
Hopfield Neural Networks ◽  
Discrete Version ◽  
Multiple Delays ◽  
Difference System ◽  
Matrix Inequalities ◽  
Delay Difference ◽  
Delay Difference System

In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference system of Hopfield neural networks in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result is applied to obtain new asymptotic stability condition for some class of delay-difference system such as delay-difference system of Hopfield neural networks with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational purposes.

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