Hopf bifurcation and stability analysis for a delayed logistic equation with additive Allee effect

Abstract

In this paper the linear stability of the delayed logistic equation with additive Allee effect is investigated. We also analyze the associated characteristic transcendental equation, to show the occurrence of Hopf bifurcation at the positive equilibrium. To determine the direction of Hopf bifurcation and the stability of bifurcating periodic solution, we use the normal form approach and a center manifold theorem. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical analysis.

Keywords

• time delay
• logistic equation
• stability
• Hopf bifurcation
• additive Allee effect