2012/05/17 by Anca Veronica Ion, Anca-Veronica Ion, Ion, Anca Veronica +3
Mathematics · Medicine · #37C75 #37G05 #37G15 #65L03 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #math.DS #msc:37C75 #msc:37G05 #msc:37G15 #msc:65L03
paper · pdf · doi:10.48550/arxiv.1205.3917
arxiv created 2012/05/17 · openalex publication_date 2012/05/17 · arxiv updated 2012/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper continues the work contained in two previous papers, devoted to the study of the dynamical system generated by a delay differential equation that models leukemia. Here our aim is to identify degenerate Hopf bifurcation points. By using an approximation of the center manifold, we compute the first Lyapunov coefficient for Hopf bifurcation points. We find by direct computation, in some zones of the parameter space (of biological significance), points where the first Lyapunov coefficient equals zero. For these we compute the second Lyapunov coefficient, that determines the type of the degenerate Hopf bifurcation.