scholarly journals Existence and exponential convergence of the positive almost periodic solution for a model of hematopoiesis

2013 ◽  
Vol 26 (1) ◽  
pp. 38-42 ◽  
Author(s):  
Hong Zhang ◽  
Mingquan Yang ◽  
Lijuan Wang
Keyword(s):  
Periodic Solution ◽  
Exponential Convergence ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution

scholarly journals Positive Almost Periodic Solution for a Model of Hematopoiesis with Infinite Time Delays and a Nonlinear Harvesting Term

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Zhou ◽  
Wen Wang ◽  
Zongfu Zhou
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Lyapunov Functional ◽  
Time Delays ◽  
Exponential Convergence ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Infinite Time ◽  
Positive Almost Periodic Solution ◽  
Nonlinear Harvesting

A generalized model of Hematopoiesis with infinite time delays and a nonlinear harvesting term is investigated. By utilizing a fixed point theorem of the differential equations and constructing a suitable Lyapunov functional, we establish some conditions which guarantee the existence of a unique positive almost periodic solution and the exponential convergence of the system. Finally, we give an example to illustrate the effectiveness of our results.

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 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 GLOBAL EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR NICHOLSON’S BLOWFLIES SYSTEM WITH NONLINEAR DENSITY-DEPENDENT MORTALITY TERMS AND PATCH STRUCTURE

2017 ◽  
Vol 22 (4) ◽  
pp. 484-502 ◽  
Author(s):  
Pengyan Liu ◽  
Liang Zhang ◽  
Shitao Liu ◽  
Lifei Zheng
Keyword(s):  
Periodic Solution ◽  
Global Exponential Stability ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Patch Structure ◽  
Density Dependent ◽  
Density Dependent Mortality ◽  
Positive Almost Periodic Solution ◽  
Dependent Mortality

This paper considers a generalized Nicholson’s blowflies system with nonlinear density-dependent mortality terms and patch structure. Under appropriate conditions, we establish some criteria to ensure that the solutions of this system exist and converge globally exponentially to a positive almost periodic solution. The results complement another case of nonlinear density-dependent mortality terms in Chen and Wang [5].

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