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Zbl 0694.34057
Gopalsamy, K.; Kulenović, M.R.S.; Ladas, G.
Oscillations and global attractivity in models of hematopoiesis.
(English)
[J] J. Dyn. Differ Equations 2, No.2, 117-132 (1990). ISSN 1040-7294; ISSN 1572-9222/e

Summary: Let P(t) denote the density of mature cells in blood circulation. {\it M. C. Mackey} and {\it L. Glass} [Science 197, 287-289 (1977)] have proposed the following equations: $$\dot P(t)=\frac{\beta\sb 0\theta\sp n}{\theta\sp n+[P(t-\tau)]\sp n}-\gamma P(t)$$ and $$\dot P(t)=\frac{\beta\sb 0\theta\sp nP(t-\tau)}{\theta\sp n+[P(t-\tau)]\sp n}- \gamma P(t)$$ as models of hematopoiesis. We obtain sufficient and also necessary and sufficient conditions for all positive solutions to oscillate about their respective positive steady states. We also obtain sufficient conditions for the positive equilibrium to be a global attractor.
MSC 2000:
*34K99 Functional-differential equations
92D25 Population dynamics
34C15 Nonlinear oscillations of solutions of ODE

Keywords: hematopoiesis; global attractor

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