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Dynamics for a class of general hematopoiesis model with periodic coefficients. (English) Zbl 1120.34053

Summary: Sufficient conditions are obtained for the existence and global attractivity of a unique positive periodic solution x ˜(t) of

x ' (t)=-a(t)x(t)+b(t) 1+x n (t-τ(t)),t>0,(*)

where n>1, a and b are continuous positive periodic function. Also, some sufficient conditions are established for oscillation of all positive solutions of (*) about x ˜(t). For the proof of existence and uniqueness of x ˜(t), the method used here is better than the contraction mapping principle.

34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
34K11Oscillation theory of functional-differential equations
92C30Physiology (general)