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
2018 ◽  
Vol 13 (03) ◽  
pp. 2050058
Author(s):  
K. R. Prasad ◽  
Md. Khuddush

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.


2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Heping Ma ◽  
Jianguo Gao ◽  
Lingling Xie

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.


2014 ◽  
Vol 07 (04) ◽  
pp. 1450040 ◽  
Author(s):  
Qinglong Wang ◽  
Zhijun Liu ◽  
Zuxiong Li ◽  
Robert A. Cheke

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.


2012 ◽  
Vol 05 (03) ◽  
pp. 1250038 ◽  
Author(s):  
Yongkun Li ◽  
Li Yang

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Qinglong Wang ◽  
Zhijun Liu

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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