Oscillation and global attractivity in a periodic delay hematopoiesis model |
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Authors: | S H Saker |
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Institution: | 1. Department of Mathematics, Faculty of Science, Maqnsoura University, 35516, Mansoura, Egypt
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Abstract: | In this paper we shall consider the nonlinear delay differential equation $$p'(t) = \frac{{\beta (t)}}{{1 + p^n (t - m\omega )}} - \delta (t)p(t),$$ wherem is a positive integer, β(t) and δ(t) are positive periodic functions of period ω. In the nondelay case we shall show that (*) has a unique positive periodic solution $\bar p(t)$ , and show that $\bar p(t)$ is a global attractor all other positive solutions. In the delay case we shall present sufficient conditions for the oscillation of all positive solutions of (*) about $\bar p(t)$ , and establish sufficient conditions for the global attractivity of $\bar p(t)$ . Our results extend and improve the well known results in the autonomous case. |
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