Hopf bifurcation in a delayed logistic growth with feedback control

Abstract

In this paper, the bifurcation of the delayed logistic model with feedback control variable are investigated. By regarding the corresponding characteristic equations, the linear stability of the system is discussed and Hopf bifurcations are demonstrated, especially the stability switch is discussed in this system. By the normal form and the center manifold theory, the explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. Finally, some examples are presented to verify our main results.