876 research outputs found
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
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
Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases
Hematopoiesis is a complex biological process that leads to the production
and regulation of blood cells. It is based upon differentiation of stem cells
under the action of growth factors. A mathematical approach of this process is
proposed to carry out explanation on some blood diseases, characterized by
oscillations in circulating blood cells. A system of three differential
equations with delay, corresponding to the cell cycle duration, is analyzed.
The existence of a Hopf bifurcation for a positive steady-state is obtained
through the study of an exponential polynomial characteristic equation with
delay-dependent coefficients. Numerical simulations show that long period
oscillations can be obtained in this model, corresponding to a destabilization
of the feedback regulation between blood cells and growth factors. This
stresses the localization of periodic hematological diseases in the feedback
loop
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 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 CientÃficas 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 CientÃficas 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
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
- …