scholarly journals Unique Positive Almost Periodic Solution for Discrete Nonlinear Delay Survival Red Blood Cells Model

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Xitao Yang ◽  
Siping Tang
Keyword(s):  
Red Blood Cells ◽  
Blood Cells ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
Positive Almost Periodic Solutions ◽  
Nonlinear Delay

We obtain sufficient conditions which guarantee the global attractivity of solutions for nonlinear delay survival red blood cells model. Then, some criteria are established for the existence, uniqueness and global attractivity of positive almost periodic solutions of the almost periodic system.

POSITIVE ALMOST PERIODIC SOLUTIONS FOR THE HEMATOPOIESIS MODEL VIA THE HILBERT PROJECTIVE METRIC

2016 ◽  
Vol 95 (1) ◽  
pp. 84-93 ◽  
Author(s):  
HECHMI HATTAB
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
Uniqueness Of The Solution ◽  
Projective Metric ◽  
Hematopoiesis Model ◽  
Positive Almost Periodic Solutions

The aim of this work is to prove the existence of a positive almost periodic solution to a multifinite time delayed nonlinear differential equation that describes the so-called hematopoiesis model. The approach uses the Hilbert projective metric in a cone. With some additional assumptions, we construct a fixed point theorem to prove the desired existence and uniqueness of the solution.

scholarly journals Permanence and Almost Periodic Solutions of a Discrete Ratio-Dependent Leslie System with Time Delays and Feedback Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-31 ◽  
Author(s):  
Gang Yu ◽  
Hongying Lu
Keyword(s):  
Time Delays ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Positive Almost Periodic Solution ◽  
Ratio Dependent ◽  
Globally Attractive ◽  
Leslie System

We consider a discrete almost periodic ratio-dependent Leslie system with time delays and feedback controls. Sufficient conditions are obtained for the permanence and global attractivity of the system. Furthermore, by using an almost periodic functional Hull theory, we show that the almost periodic system has a unique globally attractive positive almost periodic solution.

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 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 Positive Almost Periodic Solutions for a Time-Varying Fishing Model with Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Xia Li ◽  
Yongkun Li ◽  
Chunyan He
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Almost Periodic Solution ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
Positive Almost Periodic Solutions

This paper is concerned with a time-varying fishing model with delay. By means of the continuation theorem of coincidence degree theory, we prove that it has at least one positive almost periodic solution.

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 SOLUTIONS FOR AN ECOLOGICAL MODEL WITH INFINITE DELAYS

2007 ◽  
Vol 50 (1) ◽  
pp. 229-249 ◽  
Author(s):  
Yonghui Xia ◽  
Jinde Cao
Keyword(s):  
Periodic Solution ◽  
Lyapunov Functional ◽  
Ecological Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Volterra Model ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Infinite Delays ◽  
Dominated Convergence

AbstractBy using Lebesgue’s dominated convergence theorem and constructing a suitable Lyapunov functional, we study the following almost-periodic Lotka–Volterra model with $M$ predators and $N$ prey of the integro-differential equations\begin{alignat*}{2} \dot{x}_i(t)\amp=x_i(t)\biggl[b_i(t)-a_{ii}(t)x_i(t)-\sum_{k=1,k\neq i}^{N}a_{ik}(t)\int_{-\infty}^tH_{ik}(t-\sigma)x_k(\sigma)\,\mathrm{d}\sigma\\ \amp\hskip45mm-\sum_{l=1}^{M}c_{il}(t)\int_{-\infty}^tK_{il}(t-\sigma)y_l(\sigma)\,\mathrm{d}\sigma\biggr],\amp\quad i\amp=1,2,\dots,N,\\ \dot{y}_j(t)\amp=y_j(t)\biggl[-r_j(t)-e_{jj}(t)y_j(t) +\sum_{k=1}^{N}d_{jk}(t)\int_{-\infty}^tP_{jk}(t-\sigma)x_k(\sigma)\,\mathrm{d}\sigma \\ \amp\hskip45mm-\sum_{l=1,l\neq j}^{M} e_{jl}(t)\int_{-\infty}^tQ_{jl}(t-\sigma)y_l(\sigma)\,\mathrm{d}\sigma\biggr],\amp\quad j\amp=1,2,\dots,M. \end{alignat*}Some sufficient conditions are obtained for the existence of a unique almost-periodic solution of this model. Several examples show that the obtained criteria are new, general and easily verifiable.

scholarly journals Almost periodic solutions of Volterra difference systems

2017 ◽  
Vol 50 (1) ◽  
pp. 320-329
Author(s):  
Halis Can Koyuncuoglu ◽  
Murat Adıvar
Keyword(s):  
Periodic Solution ◽  
Exponential Dichotomy ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Difference Systems ◽  
Volterra Systems

Abstract We study the existence of an almost periodic solution of discrete Volterra systems by means of fixed point theory. Using discrete variant of exponential dichotomy, we provide sufficient conditions for the existence of an almost periodic solution. Hence, we provide an alternative solution for the open problem proposed in the literature.

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