|
|
|||
|
||||
OverviewThis 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: IntroductionThe Hopf Bifurcation TheoremContinuation of Bifurcation Curves on the Parameter PlaneDegenerate Bifurcations in the Space of System ParametersHigh-Order Hopf Bifurcation FormulasHopf Bifurcation in Nonlinear Systems with Time DelaysBirth of Multiple Limit CyclesAppendixReferencesArthur IndexSubject IndexReadership: Nonlinear scientists, applied mathematicians, and systems engineers. Full Product DetailsAuthor: Guan Rong Chen , Jorge L Moiola , Guanrong Chen (City University of Hong Kong, Kowloon)Publisher: World Scientific Publishing Company Imprint: World Scientific Publishing Company ISBN: 9781299668171ISBN 10: 1299668178 Pages: 346 Publication Date: 01 January 1996 Audience: General/trade , General Format: Electronic book text Publisher's Status: Active Availability: In stock We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |