Abstract—This paper deals with the stability analysis and theHopf bifurcation at the equilibrium points of a logistic delay differential equation.By applying the Halanay inequality, the local stability of the logistic differential equation is discussed. The stability of bifurcation periodic solutions and the direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical examples show interesting nonlinear behavior of the logistic differential equation at the end of the paper.
Index Terms—Differential equations with delay, Hopf bifurcation, local stability, global asymptotic stability, periodic solutions.
F. Bozkurt is with the Department of Mathematics, ErciyesUniversity, Turkey (e-mail: fbozkurt@erciyes.edu.tr).
[PDF]
Cite:F. Bozkurt, "Hopf Bifurcation and Stability Analysis for A Delayed Logistic Equation," International Journal of Modeling and Optimization vol. 3, no. 3, pp. 288-292, 2013.
