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Oscillation and global attractivity in hematopoiesis model with periodic coefficients. (English) Zbl 1048.34114
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.

MSC:
34K11Oscillation theory of functional-differential equations
34K20Stability theory of functional-differential equations
92D25Population dynamics (general)
92C50Medical applications of mathematical biology
34K60Qualitative investigation and simulation of models
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References:
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