Notice of Retraction: Stability and bifurcation analysis in a Mackey-Glass system

Abstract

In this paper, the dynamics of a Mackey-Glass equation with delay are investigated. We prove that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the theory of normal form and center manifold. The global existence of multiple periodic solutions is established using a global Hopf bifurcation result given by Wu and Bendixson criterion for given by Li and l.