Skip to Main content Skip to Navigation
Journal articles

Stability analysis of an equation with two delays and application to the production of platelets

Loïs Boullu 1, 2, 3, 4, 5, * Laurent Pujo-Menjouet 1, 3, 4, 5 Jacques Bélair 2
* Corresponding author
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
ICJ - Institut Camille Jordan [Villeurbanne], Inria Grenoble - Rhône-Alpes, CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire
3 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We analyze the stability of a differential equation with two delays originating from a model for a population divided into two subpopulations, immature and mature, and we apply this analysis to a model for platelet production. The dynamics of mature individuals is described by the following nonlinear differential equation with two delays: x'(t) = −γx(t) + g(x(t − τ1)) − g(x(t − τ1 − τ2))e(−γ τ2). The method of D-decomposition is used to compute the stability regions for a given equilibrium. The centre manifold theory is used to investigate the steady-state bifurcation and the Hopf bifurcation. Similarly, analysis of the centre manifold associated with a double bifurcation is used to identify a set of parameters such that the solution is a torus in the pseudo-phase space. Finally, the results of the local stability analysis are used to study the impact of an increase of the death rate γ or of a decrease of the survival time τ2 of platelets on the onset of oscillations. We show that the stability is lost through a small decrease of survival time (from 8.4 to 7 days), or through an important increase of the death rate (from 0.05 to 0.625 1/day).
Document type :
Journal articles
Complete list of metadata

Cited literature [27 references]  Display  Hide  Download

https://hal.inria.fr/hal-02109546
Contributor : Loïs Boullu <>
Submitted on : Thursday, April 25, 2019 - 1:54:56 AM
Last modification on : Monday, June 28, 2021 - 2:26:07 PM

File

DCDS-S_platelet_arxiv.pdf
Files produced by the author(s)

Identifiers

Citation

Loïs Boullu, Laurent Pujo-Menjouet, Jacques Bélair. Stability analysis of an equation with two delays and application to the production of platelets. Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, In press, pp.1-24. ⟨10.3934/dcdss.2020131⟩. ⟨hal-02109546⟩

Share

Metrics

Record views

230

Files downloads

1144