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

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

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

On the global dynamic behaviour for a generalized haematopoiesis model with almost periodic coefficients and oscillating circulation loss rate

A generalized non-linear nonautonomous model for the haematopoiesis (cell production) with several delays and an oscillating circulation loss rate is studied. We prove a fixed point theorem in abstract cones, from which different results on existence and uniqueness of positive almost periodic solutions are deduced. Moreover, some criteria are given to guarantee that the obtained positive almost periodic solution is globally exponentially stable.Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Balderrama, Rocio Celeste. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin

Almost periodic solutions for an impulsive delay Nicholson’s blowflies model

AbstractBy means of the contraction mapping principle and Gronwall–Bellman’s inequality, we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay Nicholson’s blowflies model. The main results are illustrated by an example

New results on the positive pseudo almost periodic solutions for a generalized model of hematopoiesis

The main purpose of this paper is to study the existence and global exponential stability of the positive pseudo almost periodic solutions for a generalized model of hematopoiesis with multiple time-varying delays. By using the exponential dichotomy theory and fixed point theorem, some sufficient conditions are given to ensure that all solutions of this model converge exponentially to the positive pseudo almost periodic solution, which improve and extend some known relevant results. Moreover, an example and its numerical simulation are given to illustrate the theoretical results

Multiplicity of positive periodic solutions for a discrete impulsive blood cell production model

In this paper, we investigate the multiplicity of positive periodic solutions of a discrete blood cell production model with impulse effects. This model is described by periodic coefficients and time delays, as well as nonlinear feedback with exponential terms. By employing the Krasnosel'skii fixed point theorem, we establish a sufficient condition for the existence of at least two positive periodic solutions. To this end, we construct solution transformation between an impulsive delay difference equation and the corresponding nonimpulsive delay difference equation. Aditionally, a solution representation of the positive periodic solution of the blood cell production model is presented. Moreover, a numerical example and its simulations are given to illustrate the main result