On the existence and exponential attractivity of a unique positive almost periodic solution to an impulsive hematopoiesis model with delays

In this paper, a generalized model of hematopoiesis with delays and impulses is considered. By employing the contraction mapping principle and a novel type of impulsive delay inequality, we prove the existence of a unique positive almost periodic solution of the model. It is also proved that, under the proposed conditions in this paper, the unique positive almost periodic solution is globally exponentially attractive. A numerical example is given to illustrate the effectiveness of the obtained results.Comment: Accepted for publication in AM

Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis

By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.The research of Juan J. Nieto has been partially supported by Ministerio de Educacion y Ciencia and FEDER, project MTM2007-61724S

Global Attractivity of a Circadian Pacemaker Model in a Periodic Environment

In this paper, we propose a delay differential equation with continuous periodic parameters to model the circadian pacemaker in a periodic environment. First, we show the existence of a positive periodic solution by using the theory of coincidence degree. Then we establish the global attractivity of the periodic solution under two su±cient conditions. These conditions are easily verifiable and are independent of each other. Some numerical simulations are also performed to demonstrate the main results

Existence and global attractivity of positive periodic solutions for the impulsive delay Nicholson's blowflies model

AbstractIn this paper we shall consider the following nonlinear impulsive delay population model:(0.1)x′(t)=-δ(t)x(t)+p(t)x(t-mω)e-α(t)x(t-mω)a.e. t>0,t≠tk,x(tk+)=(1+bk)x(tk),k=1,2,…,where m is a positive integer, δ(t), α(t) and p(t) are positive periodic continuous functions with period ω>0. In the nondelay case (m=0), we show that (0.1) has a unique positive periodic solution x*(t) which is globally asymptotically stable. In the delay case, we present sufficient conditions for the global attractivity of x*(t). Our results imply that under the appropriate linear periodic impulsive perturbations, the impulsive delay equation (0.1) preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results

On the Oscillation of the Generalized Food-Limited Equations with Delay

- The objective of the paper is to find conditions for the oscillation of the food-limited equation. We established conditions for the oscillation of all solutions of the generalized foodlimited equation by transforming the equation to a non-linear delay differential equation and then to a scalar delay differential equation and using the property of the scalar delay differential equation to obtain our result. Similarly we establish conditions for the oscillation of all solutions of the foodlimited equation with several delays by transforming the equation to a scalar differential equation to obtain the oscillatory property

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

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