Global attractivity of periodic solution in a model of hematopoiesis

Oscillation and global attractivity in hematopoiesis model with periodic coefficients

In this paper we shall consider the nonlinear delay differential equation p0ðtÞ 1⁄4 bðtÞp mðt kxÞ 1þ pnðt kxÞ cðtÞpðtÞ; ð Þ where k is a positive integer, bðtÞ and cðtÞ are positive periodic functions of period x. In the nondelay case we shall show that (*) has a unique positive periodic solution pðtÞ, and we will study the global attractivity of pðtÞ. In the delay case we shall establish some ...

Global attractivity of positive periodic solution to periodic Lotka – Volterra competition systems with pure delay ✩

We consider a periodic Lotka–Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems) ẋi (t)= xi(t) [ ri (t)− n ∑ j=1 aij (t)xj ( t − τij (t) )] , i = 1,2, . . . , n. (∗) We establish some 3/2-type criteria for global attractivity of a positive periodic solution of the system, which generalize the well-known Wright’s 3/2 criteria for the autonomous delay l...

Global Attractivity and Periodic Solution of a Discrete Multispecies Cooperation and Competition Predator-Prey System

On the global attractivity controversy for a delay model of hematopoiesis

Recently, particular counterexamples were constructed to some theorems of a previous paper, concerning the global attractivity of the positive equilibrium for the delay equation 0096-3 doi:10 * Ad E-m _ pðtÞ 1⁄4 bp mðt sÞ 1þ pnðt sÞ cpðtÞ: The purpose of this note is to explore the underlying phenomenon from a more general point of view, and to give an explanation of the situation. A theorem is...

Global Attractivity and Periodic Nature of a Difference Equation

Our goal in this paper is to investigate the global stability character and the periodicity of the solutions of the difference equation Where the initial conditions x ,x ,...,x are arbitrary positive real numbers, r = max{l, k} is nonnegative integer –r –r+1 0 and a, b, c, d are positive constants.