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Zaghrout, A.; Ammar, A.; El-Sheikh, M. M. A.

Oscillations and global attractivity in delay differential equations of population dynamics. (English) Zbl 0848.92018

Appl. Math. Comput. 77, No. 2-3, 195-204 (1996).
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.

Cited in 19 Documents

MSC:

92D25 Population dynamics (general)
34K25 Asymptotic theory of functional-differential equations
34K11 Oscillation theory of functional-differential equations
92C30 Physiology (general)

Keywords:

delay differential equations; positive solutions; positive steady state; density of mature cells; blood circulation; immature cells; bone marrow
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\textit{A. Zaghrout} et al., Appl. Math. Comput. 77, No. 2--3, 195--204 (1996; Zbl 0848.92018)
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References:

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