HOPF BIFURCATION ANALYSIS
A Frequency Domain Approach

Jorge L Moiola  (Univ. Nacional del Sur, Argentina)
Guanrong Chen (Univ. Houston, Texas, USA)

This book is devoted to the frequency domain approach, for both regular and
degenerate Hopf bifurcation analyses. Besides showing that the time and
frequency domain approaches are in fact equivalent, the fact that many
significant results and computational formulas obtained in the studies of
regular and degenerate Hopf bifurcations from the time domain approach can be
translated and reformulated into the corresponding frequency domain setting, and
be reconfirmed and rediscovered by using the frequency domain methods, is also
explained. The description of how the frequency domain approach can be used to
obtain several types of standard bifurcation conditions for general nonlinear
dynamical systems is given as well as is demonstrated a very rich pictorial
gallery of local bifurcation diagrams for nonlinear systems under simultaneous
variations of several system parameters. In conjunction with this graphical
analysis of local bifurcation diagrams, the defining and nondegeneracy
conditions for several degenerate Hopf bifurcations is presented. With a great
deal of algebraic computation, some higher-order harmonic balance approximation
formulas are derived, for analyzing the dynamical behavior in small
neighborhoods of certain types of degenerate Hopf bifurcations that involve
multiple limit cycles and multiple limit points of periodic solutions. In
addition, applications in chemical, mechanical and electrical engineering as
well as in biology are discussed. This book is designed and written in a style
of research monographs rather than classroom textbooks, so that the most recent
contributions to the field can be included with references.

Contents:
  Introduction
  The Hopf Bifurcation Theorem
  Continuation of Bifurcation Curves on the Parameter Plane
  Degenerate Bifurcations in the Space of System Parameters
  High-Order Hopf Bifurcation Formulas
  Hopf Bifurcation in Nonlinear Systems with Time Delays
  Birth of Multiple Limit Cycles
  Appendix
  References
  Arthur Index
  Subject Index

Readership: Nonlinear scientists, applied mathematicians, and systems engineers.

  344ppPub. date: Apr 1996
  ISBN 981-02-2628-4US$55 / £38