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Permanence, oscillation and attractivity of the discrete hematopoiesis model with variable coefficients. (English) Zbl 1125.39002

The authors study a periodic discrete Mackey-Glass equation
\[ p_{n+1}-p_n= -\delta_np_n+\frac{\beta_n}{1+p_{n-\omega}^m}, \]
where \(\delta_n\in(0,1)\), \(\beta_n>0\) are \(\omega\)-periodic sequences and \(m>1\).
For positive initial values it is shown that every solution is positive, permanent and entering a bounded set. Moreover, every nonoscillatory solution tends to a \(\omega\)-periodic positive solution \(\bar p_n\), and conditions for \(\bar p_n\) to be the global attractor are given. Finally, some sufficient condition for the oscillation of every positive solution about \(\bar p_n\) are established.

MSC:

39A14 Partial difference equations
92D25 Population dynamics (general)
39A12 Discrete version of topics in analysis
39A20 Multiplicative and other generalized difference equations
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