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.

Existence and exponential stability of almost periodic positive solution for host-macroparasite difference model

2016 ◽  
Vol 09 (02) ◽  
pp. 1650028
Author(s):  
Zhijian Yao
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Exponential Stability ◽  
Positive Solution ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Difference Model

This paper is concerned with a host-macroparasite difference model. By applying the contraction mapping fixed point theorem, we prove the existence of unique almost periodic positive solution. Moreover, we investigate the exponential stability of almost periodic solution by means of Lyapunov functional.

scholarly journals On the Almost Periodic Solutions of Differential Equations on Hilbert Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Nguyen Thanh Lan
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Necessary And Sufficient

For the differential equation , on a Hilbert space , we find the necessary and sufficient conditions that the above-mentioned equation has a unique almost periodic solution. Some applications are also given.

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 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 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.

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.

scholarly journals An Almost Periodic Lasota-Wazewska Dynamic Model on Time Scales

2018 ◽  
pp. 17-32
Author(s):  
Zhijian Yao
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Positive Solution ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Iterative Sequence ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
The Fixed Point Theorem

This paper deals with almost periodicity of Lasota-Wazewska dynamic equation on time scales. By applying a method based on the fixed point theorem of decreasing operator, we establish sufficient conditions for the existence of a unique almost periodic positive solution. We also give iterative sequence which converges to almost periodic positive solution. Moreover, we investigate the exponential stability of almost periodic solution by means of Gronwall inequality. Our study unifies differential and difference equations.

Dynamics of Almost Periodic Solution for a Delayed Facultative Mutualism Model Involving Negative Feedback Terms

2018 ◽  
Vol 19 (3-4) ◽  
pp. 309-320
Author(s):  
Li Yang ◽  
Zunguang Guo
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Analytical Techniques ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Mawhin’S Continuation Theorem ◽  
Facultative Mutualism ◽  
Positive Almost Periodic Solution

AbstractBy using some new analytical techniques, modified inequalities and Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the boundedness of the solution and the existence of at least one positive almost periodic solution of a kind of two-species model of facultative mutualism with time delays. Further, the global asymptotic stability of the positive almost periodic solution of this model is also considered. Some examples and numerical simulations are also given to illustrate the main results of this paper.

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