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Zbl 1048.34114
Saker, S. H.
Oscillation and global attractivity in hematopoiesis model with periodic coefficients. (English)
[J] Appl. Math. Comput. 142, No. 2-3, 477-494 (2003). ISSN 0096-3003

The author considers the following nonlinear delay differential equation $$p'(t)= {\beta(t) p^m(t- k\omega)\over 1+ p^n(t- k\omega)}- \gamma(t) p(t),\tag1$$ where $k$ is a positive integer, $\beta(t)$ and $\gamma(t)$ are positive periodic functions of period $\omega$. The main result for the nondelay case is Theorem 2.1, where the author proves that (1) has a unique positive periodic solution $\overline p(t)$. He also studies the global attractivity of $\overline p(t)$. In the delay case, sufficient conditions for the oscillation of all positive solutions to (1) about $\overline p(t)$ are given, also some sufficient conditions for the global attractivity of $\overline p(t)$ are established. It should be noted that (1) is a modification of an equation proposed as a model of hematopoiesis. Similar equations are also used as models in population dynamics.
[V. Petrov (Plovdiv)]

MSC 2000:: *34K11 Oscillation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
92D25 Population dynamics
92C50 Medical appl. of mathematical biology
34K60 Applications of functional-differential equations

Keywords: oscillation; global attractivity; hematopoiesis

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