Abstract
The main purpose of this paper is to study the existence and global exponen- tial 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 peri- odic solution, which improve and extend some known relevant results. Moreover, an example and its numerical simulation are given to illustrate the theoretical results.
Highlights
In a classic study of population dynamics, the following delay differential equation model x (t) = −a(t)x(t) + K ∑ i=1 bi 1(t)xm(t − τi(t)) + xn(t − τi(t)) (1.1)has been used by [4, 9] to describe the dynamics of hematopoiesis
By Lemma 2.4, we obtain that the system (3.3) has exactly one pseudo almost periodic solution
It is easy to check that the results in [12, 13, 18] are invalid for the global exponential stability of positive pseudo almost periodic solution of (4.1) since τ1(t) = 2e−t4 sin2 t and τ2(t) = 2e−t6 sin2 t are pseudo almost periodic functions, not almost periodic
Summary
In a classic study of population dynamics, the following delay differential equation model x (t). The author in [10] obtained a new sufficient condition of the existence and uniqueness of positive pseudo almost periodic solution for equation (1.1) with m = 0, which can be described as follows: x i=1. It is worthwhile to continue to investigate the existence and global exponential stability of positive pseudo almost periodic solutions of (1.1) without m = 0. Motivated by the above discussions, in this paper we consider the existence, uniqueness and global exponential stability of positive pseudo almost periodic solutions of (1.1). In this present paper, a new approach will be developed to obtain a delay-independent condition for the global exponential stability of the positive pseudo almost periodic solutions of (1.1), and the exponential convergence rate can be unveiled.
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