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

TL;DR

This paper numerically investigates the Bautin bifurcation in a delay differential equation modeling leukemia, confirming its occurrence near a codimension-two Hopf bifurcation point through parameter variation and numerical integration.

Contribution

It provides the first numerical evidence of a Bautin bifurcation in a leukemia model with delay differential equations near a codimension-two Hopf point.

Findings

Confirmed Bautin bifurcation near the Hopf point

Numerical integration supports bifurcation occurrence

Highlights complex dynamics in leukemia delay models

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.