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

Abstract

In a previous work we investigated the existence of Hopf degenerate bifurcation points for a differential delay equation modeling leukemia and we actually found Hopf points of codimension two for the considered problem. If around the parameters corresponding to such a point we vary two parameters (the considered problem has five parameters), then a Bautin bifurcation should occur. In this work we chose a Hopf point of codimension two for the considered problem and perform numerical integration for parameters chosen in a neighborhood of the bifurcation point parameters. The results show that, indeed, we have a Bautin bifurcation in the chosen point.

arXiv commentTo be presented at CAIM 2012 (Conference on Applied and Industrial Mathematics), 23-25 August 2012, Chisinau, Republic of Moldova

References in corpus (5)

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