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Oscillation and global attractivity in hematopoiesis model with periodic coefficients. (English) Zbl 1048.34114

The author considers the following nonlinear delay differential equation

p ' (t)=β(t)p m (t-kω) 1+p n (t-kω)-γ(t)p(t),(1)

where k is a positive integer, β(t) and γ(t) are positive periodic functions of period ω. The main result for the nondelay case is Theorem 2.1, where the author proves that (1) has a unique positive periodic solution p ¯(t). He also studies the global attractivity of p ¯(t). In the delay case, sufficient conditions for the oscillation of all positive solutions to (1) about p ¯(t) are given, also some sufficient conditions for the global attractivity of p ¯(t) are established. It should be noted that (1) is a modification of an equation proposed as a model of hematopoiesis. Similar equations are also used as models in population dynamics.

MSC:
34K11Oscillation theory of functional-differential equations
34K20Stability theory of functional-differential equations
92D25Population dynamics (general)
92C50Medical applications of mathematical biology
34K60Qualitative investigation and simulation of models