Hopf Bifurcation Analysis: A Frequency Domain Approach (Series on Nonlinear Science, Series a, Vol 21)

Moiola, Jorge L.

ISBN 10: 9810226284 / ISBN 13: 9789810226282

Published by World Scientific Publishing Company, 1996

About this Item

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Seller Inventory # ERICA82998102262846

Bibliographic Details

• Title: Hopf Bifurcation Analysis: A Frequency Domain Approach (Series on Nonlinear Science, Series a, Vol 21)
• Publisher: World Scientific Publishing Company
• Publication Date: 1996
• Language: English
• ISBN 10: 9810226284
• ISBN 13: 9789810226282
• Binding: Hardcover
• Condition: Very Good
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

About this title

Synopsis

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.