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Global behavior of a discrete haematopoiesis model with several delays. (English) Zbl 1277.39024
Summary: In this paper, we study the difference equation $\Delta y_n=-\alpha y_n+\sum_{j=1}^n \frac{\beta_jy_{n-k_j}}{1+y^p_{n-k_j}},$ where $$\alpha\in (0,1)$$, $$p\in(1,\infty)$$, $$\beta_j\in(1,\infty)$$, $$k_j\in\{1,2,\ldots\,\}$$, $$j=1,2,\ldots, m$$, $$\sum_{j=1}^m \beta_j=\beta$$, $$\beta\in (\alpha,\infty$$. We give some sufficient conditions which guarantee that all solutions of the equation are oscillatory, or that the positive equilibrium of the equation is globally asymptotically stable.

##### MSC:
 39A21 Oscillation theory for difference equations 39A30 Stability theory for difference equations 92B05 General biology and biomathematics
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##### References:
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