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.

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.

scholarly journals Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Hong Zhang ◽  
Mingquan Yang
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

Shunting inhibitory cellular neural networks (SICNNs) are considered with the introduction of continuously distributed delays in the leakage (or forgetting) terms. By using the Lyapunov functional method and differential inequality techniques, some sufficient conditions for the existence and exponential stability of almost periodic solutions are established. Our results complement with some recent ones.

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.

scholarly journals Existence and Global Uniform Asymptotic Stability of Almost Periodic Solutions for Cellular Neural Networks with Discrete and Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Zongyi Hou ◽  
Hongying Zhu ◽  
Chunhua Feng
Keyword(s):  
Differential Equation ◽  
Neural Networks ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Lyapunov Functionals ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniform Asymptotic Stability

This paper discusses the existence and global uniform asymptotic stability of almost periodic solutions for cellular neural networks (CNNS). By utilizing the theory of the almost periodic differential equation and the Lyapunov functionals method, some sufficient conditions are obtained to ensure the existence and global uniform asymptotic stability. An example is given to illustrate the effectiveness of the main results.

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