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Zbl 0848.92018
Zaghrout, A.; Ammar, A.; El-Sheikh, M.M.A.
Oscillations and global attractivity in delay differential equations of population dynamics. (English)
[J] Appl. Math. Comput. 77, No.2-3, 195-204 (1996). ISSN 0096-3003

Summary: The oscillatory and asymptotic behavior of all positive solutions of $$x'(t) = \beta_0 \theta^n/(\theta^n + x^n (t - \tau)) - \gamma x(t)$$ about the positive steady state $x^*$ are studied, where $x(t)$ denotes the density of mature cells in blood circulation, $\tau$ is the time delay between the production of immature cells in the bone marrow, and $\beta_0$, $\theta^n$, $\gamma$ are positive constants.

MSC 2000:: *92D25 Population dynamics
34K25 Asymptotic theory of functional-differential equations
34K11 Oscillation theory of functional-differential equations
92C30 Physiology

Keywords: delay differential equations; positive solutions; positive steady state; density of mature cells; blood circulation; immature cells; bone marrow

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