Hopf points of codimension two in a delay differential equation modeling leukemia

Abstract

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.

References in corpus (4)

• Lyapunov Coefficients for Degenerate Hopf Bifurcations
• On the Bautin bifurcation for systems of delay differential equations
• Stability of equilibrium and periodic solutions of a delay equation modeling leukemia
• New results concerning the stability of equilibria of a delay differential equation modeling leukemia

Cited by in corpus (1)

• Numerical investigation of the Bautin bifurcation in a delay differential equation modeling leukemia