Existence and global attractivity of unique positive periodic solution for a Lasota–Wazewska model

Abstract

In this paper we consider the Lasota–Wazewska model x ′ ( t ) = - a ( t ) x ( t ) + ∑ i = 1 m p i ( t ) e - q i ( t ) x ( 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 n to x ˜ , where { x n } is a successive sequence, but also show that x ˜ is a global attractor of all other positive solutions.