Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models

Xiao Wang; Zhixiang Li

Xiao Wang ; Zhixiang Li

Open Mathematics, Tome 5 (2007), p. 397-414 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we discuss the special diffusive hematopoiesis model $\frac{\partial P (t, x)}{\partial t} = Δ P (t, x) - γ P (t, x) + \frac{β P (t - τ, x)}{1 + P^{n} (t - τ, x)}$ with Neumann boundary condition. Sufficient conditions are provided for the global attractivity and oscillation of the equilibrium for Eq. (*), by using a new theorem we stated and proved. When P(t, χ) does not depend on a spatial variable χ ∈ Ω, these results are also true and extend or complement existing results. Finally, existence and stability of the Hopf bifurcation for Eq. (*) are studied.

Publié le : 2007-01-01

Zbl 1214.35006

EUDML-ID : urn:eudml:doc:269168

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     author = {Xiao Wang and Zhixiang Li},
     title = {Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models},
     journal = {Open Mathematics},
     volume = {5},
     year = {2007},
     pages = {397-414},
     zbl = {1214.35006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0042-5}
}

Xiao Wang; Zhixiang Li. Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models. Open Mathematics, Tome 5 (2007) pp. 397-414. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0042-5/

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