Abstract
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.
Highlights
−αh t β hn t − τ, t ≥ 0, 1.1 where α, β, τ > 0, n ∈ 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
H t denotes the density of mature cells in blood circulation at time t and τ 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 α, and the flux of the cells into the circulation from the stem cell compartment depends on the density of mature cells at the previous time t − τ
Summary
−αh t β hn t − τ , t ≥ 0, 1.1 where α, β, τ > 0, n ∈ 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. Some dynamical systems which describe real phenomena are characterized by the fact that at certain moments in their evolution, they undergo rapid changes Most notably, this takes place due to certain seasonal effects such as weather, resource availability, food supplies, and mating habits. Theory of impulsive delay differential equations is being recognized to be richer than the corresponding theory of ordinary differential equations and to represent a more natural framework for mathematical modeling of some relevant real-world phenomena This justifies the intensive investigation of this type of equations in the recent years. The aim of this paper is to establish sufficient conditions for the existence and exponential stability of positive almost periodic solution of nonlinear impulsive delay model of hematopoiesis of form 1.2.
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