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Center Manifold Analysis of Delayed Lienard Equation and Its ApplicationsZhao, Siming 14 January 2010 (has links)
Lienard Equations serve as the elegant models for oscillating circuits. Motivated
by this fact, this thesis addresses the stability property of a class of delayed Lienard
equations. It shows the existence of the Hopf bifurcation around the steady state.
It has both practical and theoretical importance in determining the criticality of the
Hopf bifurcation. For such purpose, center manifold analysis on the bifurcation line
is required. This thesis uses operator differential equation formulation to reduce the
infinite dimensional delayed Lienard equation onto a two-dimensional manifold on
the critical bifurcation line. Based on the reduced two-dimensional system, the so
called Poincare-Lyapunov constant is analytically determined, which determines the
criticality of the Hopf bifurcation. Numerics based on a Matlab bifurcation toolbox
(DDE-Biftool) and Matlab solver (DDE-23) are given to compare with the theoretical
calculation. Two examples are given to illustrate the method.
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Oscillations dans des équations de Liénard et des équations d'évolution semi-linéaires / No English title availableBoudjema, Souhila 10 September 2013 (has links)
Les principaux résultats obtenus dans ce travail concernent l’existence et l’unicité des solutions de différents types de l’équation de Liénard forcée et des résultats de dépendance pour les solutions S-asymptotiquement w-périodiques d’équations d’évolution. Pour réaliser notre objectif, nous utilisons des outils d’analyse fonctionnelle non linéaire et des résultats sur des équations linéaire. / No English summary available.
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