Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 127510 10 pages doi 2009 127510 Research Article Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis J. O. Alzabut 1 J. J. Nieto 2 and G. Tr. Stamov3 1 Department of Mathematics and Physical Sciences Prince Sultan University . Box 66833 Riyadh 11586 Saudi Arabia 2 Departamento de Analisis Matematico Universidad de Santiago de Compostela Santiago de Compostela 15782 Spain 3 Department of Mathematics Technical University Sofia 8800 Sliven Bulgaria Correspondence should be addressed to J. O. Alzabut jalzabut@ Received 15 March 2009 Revised 28 June 2009 Accepted 30 August 2009 Recommended by Donal O Regan 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. Copyright 2009 J. O. Alzabut et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The nonlinear delay differential equation . fi hạt ah t 1 h t - T f - 0 where a fi T 0 n e N has been proposed by Mackey and Glass 1 as an appropriate model of hematopoiesis that describes the process of production of all types of blood cells generated by a remarkable self-regulated system that is responsive to the demands put upon it. In medical terms hự denotes the density of mature cells in blood circulation at time t and T is the time delay between the production of immature cells in the bone marrow and their maturation for release in circulating bloodstream. It is assumed that the cells are lost from the circulation at a rate a and the flux of the cells into the circulation from the stem .