scholarly journals Four positive periodic solutions of a discrete time Lotka-Volterra competitive system with harvesting terms

2011 ◽  
Vol 31 (2) ◽  
pp. 257 ◽  
Author(s):  
Xinggui Liu ◽  
Yaping Ren ◽  
Yongkun Li
Keyword(s):  
Periodic Solutions ◽  
Discrete Time ◽  
Positive Periodic Solutions ◽  
Competitive System

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 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 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 Positive Periodic Solutions in a Discrete Time Three Species Competition System

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Changjin Xu ◽  
Yusen Wu
Keyword(s):  
Periodic Solutions ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Analogue ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Competition System

A periodic discrete time three species competition system is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous nonautonomous three species competition system is proposed. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive periodic solutions of the model are obtained.

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