eng
International Academy of Ecology and Environmental Sciences
Computational Ecology and Software
2220-721X
2015-06-1
5
2
175
186
5
article
Hopf bifurcation and stability analysis for a delayed logistic equation
with additive Allee effect
E.M. Elabbasy
emelabbasy@mans.edu.eg
1
Waleed A.I. Elmorsi
waleed_maths@yahoo.com
1
University of Mansoura, Mansoura, Egypt
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.
http://www.iaees.org/publications/journals/ces/articles/2015-5(2)/Hopf-bifurcation-and-stability-analysis-for-delayed-logistic-equation.pdf
time delay
logistic equation
stability
Hopf bifurcation
additive Allee effect