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

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu ◽  
Yiping Chen
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
System A ◽  
Analytical Results

We consider the dynamic behaviors of a discrete competitive system. A good understanding of the permanence, existence, and global stability of positive periodic solutions is gained. Numerical simulations are also presented to substantiate the analytical results.

scholarly journals Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu
Keyword(s):  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Delay ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Discrete Function ◽  
Species Population

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

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 Global exponential stability of positive periodic solutions for a cholera model with saturated treatment

2018 ◽  
Vol 23 (5) ◽  
pp. 619-641
Author(s):  
Hongzheng Quana ◽  
Xueyong Zhoub ◽  
Jianzhou Liua
Keyword(s):  
Exponential Stability ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Incidence Rate ◽  
Global Exponential Stability ◽  
Positive Periodic Solutions ◽  
Treatment Function ◽  
Novel Method ◽  
Saturated Treatment ◽  
Theoretical Results

In this paper, we consider a cholera model with periodic incidence rate and saturated treatment function. Under certain conditions, we establish a criterion on the global exponential stability of positive periodic solutions for this model by using a novel method. We illustrate our theoretical results with numerical simulations by using Matlab.

scholarly journals Positive Periodic Solutions of a Periodic Discrete Competitive System Subject to Feedback Controls

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ronghua Tan ◽  
Zuxiong Li ◽  
Qinglong Wang ◽  
Zhijun Liu
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Feedback Controls ◽  
Numerical Investigations ◽  
Analysis Techniques ◽  
Discrete Inequality

Species living in a fluctuating medium and human exploitation activities might result in the duration of continuous changes. Such changes can be well-approximated as feedback controls. In this contribution a periodic discrete competitive system subject to feedback controls is proposed. By using the methods of discrete inequality, fixed point theorem, and analysis techniques, a good understanding of the existence and global asymptotic stability of positive periodic solutions is obtained. Some numerical investigations are provided to verify our analytical results.

scholarly journals Global Positive Periodic Solutions for Periodic Two-Species Competitive Systems with Multiple Delays and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Liu Yang ◽  
Yunhui Zeng
Keyword(s):  
Global Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Multiple Delays ◽  
Positive Periodic Solutions ◽  
Analysis Techniques ◽  
Competitive Systems ◽  
Sufficiency Theorems

A set of easily verifiable sufficient conditions are derived to guarantee the existence and the global stability of positive periodic solutions for two-species competitive systems with multiple delays and impulses, by applying some new analysis techniques. This improves and extends a series of the well-known sufficiency theorems in the literature about the problems mentioned previously.

scholarly journals Dynamic Behaviors of a Competitive System with Beddington-DeAngelis Functional Response

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Shengbin Yu ◽  
Fengde Chen
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Functional Response ◽  
Recent Literature ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
Partial Extinction

This article studies a competitive system with Beddington-DeAngelis functional response and establishes sufficient conditions on permanence, partial extinction, and the existence of a unique almost periodic solution for the system. The results supplement and generalize the main conclusions in recent literature. Numerical simulations have been presented to validate the analytical results.

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