Existence and global attractivity of unique positive periodic solution for a model of hematopoiesis

Abstract

In this paper, we consider the generalized model of hematopoiesis x ′ ( t ) = − a ( t ) x ( t ) + ∑ i = 1 m b i ( t ) 1 + x n ( t − τ i ( t ) ) . By using a fixed point theorem, some criteria are established for the existence of the unique positive ω-periodic solution x ˜ of the above equation. In particular, we not only give the conclusion of convergence of x k to x ˜ , where { x k } is a successive sequence, but also show that x ˜ is a global attractor of all other positive solutions.