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.

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 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 solution of Nicholson's blowflies model with linear harvesting term and impulsive effects

2015 ◽  
Vol 08 (03) ◽  
pp. 1550053
Author(s):  
Zhijian Yao
Keyword(s):  
Fixed Point ◽  
Positive Solution ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Nicholson’S Blowflies Model ◽  
Linear Harvesting Term

This paper is concerned with impulsive Nicholson's blowflies model with linear harvesting term. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential convergence of the almost periodic positive solution by Lyapunov functional.

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.

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