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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-08-7000 |
| Date | 14 January 2010 |
| Creators | Zhao, Siming |
| Contributors | Kalmar-Nagy, Tamas |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis |
| Format | application/pdf |
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