scholarly journals Almost periodic solution of a discrete competitive system with delays and feedback controls

2019 ◽  
Vol 17 (1) ◽  
pp. 120-130 ◽  
Author(s):  
Yalong Xue ◽  
Xiangdong Xie ◽  
Qifa Lin
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Competitive System ◽  
Feedback Controls ◽  
Uniformly Asymptotic Stability ◽  
Positive Almost Periodic Solution

Abstract A discrete nonlinear almost periodic multispecies competitive system with delays and feedback controls is proposed and investigated. We obtain sufficient conditions to ensure the permanence of the system. Also, we establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. In additional, an example together with its numerical simulation are presented to illustrate the feasibility of the main result.

scholarly journals Almost Periodic Solution of a Multispecies Discrete Mutualism System with Feedback Controls

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Hui Zhang ◽  
Feng Feng ◽  
Bin Jing ◽  
Yingqi Li
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Positive Almost Periodic Solution ◽  
Mutualism System

We consider an almost periodic multispecies discrete Lotka-Volterra mutualism system with feedback controls. We firstly obtain the permanence of the system by utilizing the theory of difference equation. By means of constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique positive almost periodic solution which is uniformly asymptotically stable. An example together with numerical simulation indicates the feasibility of the main result.

scholarly journals Positive Almost Periodic Solutions for a Discrete Competitive System Subject to Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Qinglong Wang ◽  
Zhijun Liu ◽  
Zuxiong Li
Keyword(s):  
Periodic Solution ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Competitive System ◽  
Feedback Controls ◽  
Uniformly Asymptotic Stability ◽  
Positive Almost Periodic Solution ◽  
Positive Almost Periodic Solutions ◽  
Theoretical Results

This paper concerns a discrete competitive system subject to feedback controls. By using Lyapunov function and some preliminary lemmas, the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system are investigated. Numerical simulations suggest the feasibility of our theoretical results.

scholarly journals Almost Periodic Solution of a Discrete Schoener’s Competition Model with Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Hui Zhang ◽  
Yingqi Li ◽  
Bin Jing ◽  
Xiaofeng Fang ◽  
Jing Wang
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Competition Model ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
Globally Attractive

We consider an almost periodic discrete Schoener’s competition model with delays. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result.

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 Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanhong Zhi ◽  
Zunling Ding ◽  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Time Scales ◽  
Cluster Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Enterprise Cluster

We present a model with feedback controls based on ecology theory, which effectively describes the competition and cooperation of enterprise cluster in real economic environments. Applying the comparison theorem of dynamic equations on time scales and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the existence of uniformly asymptotically stable almost periodic solution of the system are obtained.

Dynamics of a non-autonomous ratio-dependent predator—prey system

2003 ◽  
Vol 133 (1) ◽  
pp. 97-118 ◽  
Author(s):  
Meng Fan ◽  
Qian Wang ◽  
Xingfu Zou
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Positive Periodic Solution ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Predator Prey ◽  
Prey System ◽  
Autonomous Case ◽  
Positive Almost Periodic Solution ◽  
Ratio Dependent

We investigate a non-autonomous ratio-dependent predator–prey system, whose autonomous versions have been analysed by several authors. For the general non-autonomous case, we address such properties as positive invariance, permanence, non-persistence and the globally asymptotic stability for the system. For the periodic and almost-periodic cases, we obtain conditions for existence, uniqueness and stability of a positive periodic solution, and a positive almost-periodic solution, respectively.

scholarly journals Positive Almost Periodic Solution on a Nonlinear Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Ni Hua ◽  
Tian Li-xin ◽  
Liu Xun
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Equation ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
The Stability

We study the following nonlinear equationdx(t)/dt=x(t)[a(t)-b(t)xα(t)-f(t,x(t))]+g(t), by using fixed point theorem, the sufficient conditions of the existence of a unique positive almost periodic solution for above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the unique positive almost periodic solution are derived.

Almost periodic oscillations in a generalized Mackey–Glass model of respiratory dynamics with several delays

2014 ◽  
Vol 07 (03) ◽  
pp. 1450029 ◽  
Author(s):  
Tianwei Zhang
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Analytical Techniques ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Glass Model ◽  
Positive Almost Periodic Solution ◽  
Respiratory Dynamics

By using some analytical techniques, modified inequalities and Mawhin's continuous theorem of coincidence degree theory, some simple sufficient conditions for the existence of at least one positive almost periodic solution of a generalized Mackey–Glass model of respiratory dynamics are obtained. Further, the global attractivity of positive almost periodic solution of the above model is also studied. To the best of the author's knowledge, so far, the result of this paper is completely new. Finally, three examples are given to illustrate the main results in this paper.

scholarly journals Almost Periodic Solution of a Diffusive Mixed System with Time Delay and Type III Functional Response

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Qiong Liu
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Mixed System ◽  
Uniform Persistence ◽  
Almost Periodic ◽  
Globally Asymptotically Stable ◽  
Razumikhin Technique ◽  
Predator Prey Model ◽  
Positive Almost Periodic Solution

A delayed predator-prey model with diffusion and competition is proposed. Some sufficient conditions on uniform persistence of the model have been obtained. By applying Liapunov-Razumikhin technique, we will point out, under almost periodic circumstances, a set of sufficient conditions that assure the existence and uniqueness of the positive almost periodic solution which is globally asymptotically stable.

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