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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 =-δ n p n +β n 1+p n-ω m ,

where δ n (0,1), β n >0 are ω-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 ω-periodic positive solution p ¯ n , and conditions for p ¯ n to be the global attractor are given. Finally, some sufficient condition for the oscillation of every positive solution about p ¯ n are established.

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