Abdi Tadesse (PhD)Amsalu Hafte2020-12-102023-11-042020-12-102023-11-042011-01-01http://etd.aau.edu.et/handle/123456789/23926Lie nard equation serves as the elegant models for oscillating circuits. This paper addresses the stability property of a class of delayed lie nard equations. This project uses operator differential equation formulation to reduce the infinite dimensional delayed lie nard equation onto a two dimensional manifold on the critical bifurcation. Based on the reduced two dimensional systems, the so called Poincare-Lyapunov constant is analytically determined, which determines the criticality of the Hopf-bifurcation.enCenter Manifold AnalysisHopf BifurcationDelayed LienardEquationThesis