scholarly journals On the Positive Almost Periodic Solutions of a Class of Nonlinear Lotka-Volterra Type System with Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ni Hua ◽  
Tian Li-Xin ◽  
Yao Hong-Xing
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Type System ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Volterra Type ◽  
Variable Substitution ◽  
The Fixed Point Theorem ◽  
Positive Almost Periodic Solutions

With the help of the variable substitution and applying the fixed point theorem, we derive the sufficient conditions which guarantee the existence of the positive almost periodic solutions for a class of Lotka-Volterra type system. The main results improve and generalize the former corresponding results.

ALMOST PERIODICITY IN AN IMPULSIVE LOGISTIC EQUATION WITH INFINITE DELAY

2008 ◽  
Vol 01 (03) ◽  
pp. 355-360 ◽  
Author(s):  
CHUNHUA FENG ◽  
ZHENKUN HUANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Logistic Equation ◽  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic

By employing a fixed point theorem in cones, this paper investigates the existence of almost periodic solutions for an impulsive logistic equation with infinite delay. A set of sufficient conditions on the existence of almost periodic solutions of the equation is obtained.

Almost periodic solutions of nonautonomous Lotka–Volterra competitive systems with dominated delays

2015 ◽  
Vol 08 (02) ◽  
pp. 1550019 ◽  
Author(s):  
Chunhua Feng ◽  
Jianmin Huang
Keyword(s):  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Volterra System ◽  
Volterra Type ◽  
Competitive Systems

In this paper, a class of nonautonomous Lotka–Volterra type multispecies competitive systems with delays is studied. By employing Lyapunov functional, some sufficient conditions to guarantee the existence of almost periodic solutions for the Lotka–Volterra system are obtained.

scholarly journals Existence of Almost-Periodic Solutions for Lotka-Volterra Cooperative Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Kaihong Zhao
Keyword(s):  
Time Delay ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Mawhin’S Continuation Theorem ◽  
System With Time Delay ◽  
Positive Almost Periodic Solutions

This paper considers the existence of positive almost-periodic solutions for almost-periodic Lotka-Volterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

scholarly journals Pseudo Almost Periodic Solutions for HCNNs with Time-Varying Leakage Delays

2015 ◽  
Vol 1 (1) ◽  
pp. 51-69 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Periodic Solutions ◽  
Exponential Dichotomy ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Pseudo Almost Periodic Solutions ◽  
The Fixed Point Theorem ◽  
Pseudo Almost Periodic

Abstract In this paper, we consider a class of high-order cellular neural networks (HCNNs) model with time-varying delays in the leakage terms. We give some sufficient conditions which guarantee the exponential stability of pseudo almost periodic solutions for the model. The obtained results complement with some recent ones in the literature.The technique of proof involves the exponential dichotomy theory and the fixed point theorem. An illustrative example is given with an application.

scholarly journals Almost periodic solutions of a discrete Lotka-Volterra model via exponential dichotomy theory

2021 ◽  
Vol 7 (3) ◽  
pp. 3788-3801
Author(s):  
Lini Fang ◽  
◽  
N'gbo N'gbo ◽  
Yonghui Xia
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Exponential Dichotomy ◽  
Exponential Convergence ◽  
Volterra Model ◽  
Banach Fixed Point Theorem ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
The Difference ◽  
Positive Almost Periodic Solutions

<abstract><p>In this paper, we consider a discrete non-autonomous Lotka-Volterra model. Under some assumptions, we prove the existence of positive almost periodic solutions. Our analysis relies on the exponential dichotomy for the difference equations and the Banach fixed point theorem. Furthermore, by constructing a Lyapunov function, the exponential convergence is proved. Finally, a numerical example illustrates the effectiveness of the results.</p></abstract>

scholarly journals Existence of Positive Periodic Solutions for a Class ofn-Species Competition Systems with Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Peilian Guo ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
The Fixed Point Theorem

By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class ofn-species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect.

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.

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