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 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 Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

scholarly journals Two periodic solutions of neutral difference equations modelling physiological processes

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Neutral Difference Equations ◽  
First Order ◽  
Analysis Techniques ◽  
Physiological Processes

We establish existence, multiplicity, and nonexistence of periodic solutions for a class of first-order neutral difference equations modelling physiological processes and conditions. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.

scholarly journals Existence and Lyapunov Stability of Positive Periodic Solutions for a Third-Order Neutral Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng ◽  
Yueli Chen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Lyapunov Stability ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Positive Periodic Solutions ◽  
Third Order

By applying Green's function of third-order differential equation and a fixed point theorem in cones, we obtain some sufficient conditions for existence, nonexistence, multiplicity, and Lyapunov stability of positive periodic solutions for a third-order neutral differential equation.

scholarly journals Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale

2018 ◽  
Vol 36 (2) ◽  
pp. 185
Author(s):  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scale ◽  
Variable Coefficients ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations ◽  
Compact Map

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan <cite>c1</cite>.

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 PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

2010 ◽  
Vol 82 (3) ◽  
pp. 437-445 ◽  
Author(s):  
JIFENG CHU ◽  
ZIHENG ZHANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Schauder’S Fixed Point Theorem ◽  
Positive Periodic Solutions ◽  
Singular Differential Equations ◽  
Attractive Case

AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

scholarly journals Existence of Positive Periodic Solutions for a Class of Higher-Dimension Functional Differential Equations with Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhang Suping ◽  
Jiang Wei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Higher Dimension ◽  
Positive Periodic Solutions ◽  
Krasnoselskii Fixed Point Theorem ◽  
Functional Differential

By employing the Krasnoselskii fixed point theorem, we establish some criteria for the existence of positive periodic solutions of a class ofn-dimension periodic functional differential equations with impulses, which improve the results of the literature.

scholarly journals Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Zhenguo Luo ◽  
Liping Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Distributed Delays ◽  
Positive Periodic Solutions ◽  
Volterra System

By using a fixed-point theorem of strict-set-contraction, we investigate the existence of positive periodic solutions for a class of the following impulsive neutral Lotka-Volterra system with distributed delays:xi′(t)=xi(t)[ri(t)-∑j=1naij(t)xj(t)-∑j=1n‍bij(t)∫-τij0‍fij(ξ)xj(t+ξ)dξ-∑j=1n‍cij(t)∫-σij0‍gij(ξ)xj′(t+ξ)dξ],  Δxi(tk)=-Iik(xi(tk)),  i=1,2,…,n,  k=1,2,….Some verifiable criteria are established easily.

Three Positive Periodic Solutions of Nonlinear Functional Differential Equations with Impulse Effects

2011 ◽  
Vol 403-408 ◽  
pp. 1319-1321
Author(s):  
Lei Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Nonlinear Functional ◽  
Functional Differential

In this paper, a type of nonlinear functional differential equations with impulse effects are studied by using the Leggett-Williams fixed point theorem.

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