Existence and stability of positive almost periodic solutions for a competitive system on time scales

2017 ◽  
Vol 138 ◽  
pp. 65-77 ◽  
Author(s):  
Qinglong Wang ◽  
Zhijun Liu
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Competitive System ◽  
Existence And Stability ◽  
Positive Almost Periodic Solutions

Existence and uniform asymptotic stability of positive almost periodic solutions for three-species Lotka–Volterra competitive system on time scales

2018 ◽  
Vol 13 (03) ◽  
pp. 2050058
Author(s):  
K. R. Prasad ◽  
Md. Khuddush
Keyword(s):  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Functional Method ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniform Asymptotic Stability ◽  
Competitive System ◽  
Lyapunov Functional Method ◽  
Positive Almost Periodic Solutions

In this paper, we establish existence and uniform asymptotic stability of unique positive almost periodic solutions for three-species Lotka–Volterra competitive system on time scales by using Lyapunov functional method.

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.

Existence and global asymptotic stability of positive almost periodic solutions of a two-species competitive system

2014 ◽  
Vol 07 (04) ◽  
pp. 1450040 ◽  
Author(s):  
Qinglong Wang ◽  
Zhijun Liu ◽  
Zuxiong Li ◽  
Robert A. Cheke
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Global Asymptotic Stability ◽  
Differential Inequality ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Competitive System ◽  
Positive Almost Periodic Solutions ◽  
Theoretical Results

The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of positive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results.

EXISTENCE AND STABILITY OF ALMOST PERIODIC SOLUTIONS FOR NICHOLSON'S BLOWFLIES MODELS WITH PATCH STRUCTURE AND LINEAR HARVESTING TERMS OB TIME SCALES

2012 ◽  
Vol 05 (03) ◽  
pp. 1250038 ◽  
Author(s):  
Yongkun Li ◽  
Li Yang
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Patch Structure ◽  
Time Scale Calculus ◽  
Lyapunov Function Method ◽  
Existence And Stability

In this paper, by constructing a contraction mapping and using the time scale calculus theory and the Lyapunov function method, we obtain some sufficient conditions for the existence and stability of almost periodic solutions for a class of Nicholson's blowflies models with patch structure and linear harvesting terms on time scales. The results of this paper are completely new. Moreover, we present an illustrative example and numerical simulation to show the effectiveness of obtained results.

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.

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