Center manifold analysis of delayed Liénard Equation and Its applications /

Bibliographic Details
Main Author:	Zhao, Siming
Other Authors:	Kalmár-Nagy, Tamás (Thesis advisor)
Format:	Thesis eBook
Language:	English
Published:	[College Station, Tex.] : [Texas A&M University], [2010]
Subjects:	Major Aerospace Engineering. Center manifold Lienard Equation Hopf bifurcation Delay differential equation
Online Access:	Link to OAK Trust copy

Description
Abstract:	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.
Item Description:	"Major Subject: Aerospace Engineering" Title from author supplied metadata (automated record created 2010-03-12 12:08:51). Electronic resource.
Physical Description:	1 online resource.
Bibliography:	Includes bibliographical references.