Dirichlet problem for a delayed diffusive hematopoiesis model. (August 2019)

• Record Type: Journal Article
• Authors: Pan, Xuejun; Shu, Hongying; Wang, Lin; Wang, Xiang-Sheng
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 493
• Page End: 516
• Publication Date: 2019-08
• Subjects: Delayed diffusive hematopoiesis model -- Dirichlet boundary condition -- Stability -- Bifurcation -- Global Hopf branch; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.01.008
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the dynamics of a delayed diffusive hematopoiesis model with two types of Dirichlet boundary conditions. For the model with a zero Dirichlet boundary condition, we establish global stability of the trivial equilibrium under certain conditions, and use the phase plane method to prove the existence and uniqueness of a positive spatially heterogeneous steady state. We further obtain delay-independent as well as delay-dependent conditions for the local stability of this steady state. For the model with a non-zero Dirichlet boundary condition, we show that the only positive steady state is a constant solution. Results for the local stability of the constant solution are also provided. By using the delay as a bifurcation parameter, we show that the model has infinite number of Hopf bifurcation values and the global Hopf branches bifurcated from these values are unbounded, which indicates the global existence of periodic solutions.