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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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