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

Open Mathematics (2007)

- Volume: 5, Issue: 2, page 397-414
- ISSN: 2391-5455

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topXiao Wang, and Zhixiang Li. "Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models." Open Mathematics 5.2 (2007): 397-414. <http://eudml.org/doc/269168>.

@article{XiaoWang2007,

abstract = {In this paper, we discuss the special diffusive hematopoiesis model \[\frac\{\{\partial P(t,x)\}\}\{\{\partial t\}\} = \Delta P(t,x) - \gamma P(t,x) + \frac\{\{\beta P(t - \tau ,x)\}\}\{\{1 + P^n (t - \tau ,x)\}\}\]
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.},

author = {Xiao Wang, Zhixiang Li},

journal = {Open Mathematics},

keywords = {Global attractivity; Oscillation; Hopf bifurcation; delay differential equation; Neumann boundary condition; lower-upper solution pairs},

language = {eng},

number = {2},

pages = {397-414},

title = {Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models},

url = {http://eudml.org/doc/269168},

volume = {5},

year = {2007},

}

TY - JOUR

AU - Xiao Wang

AU - Zhixiang Li

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

JO - Open Mathematics

PY - 2007

VL - 5

IS - 2

SP - 397

EP - 414

AB - In this paper, we discuss the special diffusive hematopoiesis model \[\frac{{\partial P(t,x)}}{{\partial t}} = \Delta P(t,x) - \gamma P(t,x) + \frac{{\beta P(t - \tau ,x)}}{{1 + P^n (t - \tau ,x)}}\]
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.

LA - eng

KW - Global attractivity; Oscillation; Hopf bifurcation; delay differential equation; Neumann boundary condition; lower-upper solution pairs

UR - http://eudml.org/doc/269168

ER -

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