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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:
39A14Partial difference equations
92D25Population dynamics (general)
39A12Discrete version of topics in analysis
39A20Generalized difference equations
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References:
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