Hopf bifurcation analysis: a frequency domain approach
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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c1996
|
| Schriftenreihe: | World Scientific series on nonlinear science. Series A
vol. 21 |
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | xv, 326 p. ill |
| ISBN: | 9789812798633 |
Internformat
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| 520 | |a 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 | ||
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Datensatz im Suchindex
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| author | Moiola, Jorge L. |
| author_facet | Moiola, Jorge L. |
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| author_sort | Moiola, Jorge L. |
| author_variant | j l m jl jlm |
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| bvnumber | BV044635971 |
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| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044635971 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:48Z |
| institution | BVB |
| isbn | 9789812798633 |
| language | English |
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| spelling | Moiola, Jorge L. Verfasser aut Hopf bifurcation analysis a frequency domain approach Jorge L. Moiola, Guanrong Chen Singapore World Scientific Pub. Co. c1996 xv, 326 p. ill txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science. Series A vol. 21 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 Bifurcation theory Differential equations, Nonlinear / Numerical solutions Hopf-Verzweigung (DE-588)4160648-6 gnd rswk-swf Frequenzbereichsdarstellung (DE-588)4199376-7 gnd rswk-swf Hopf-Verzweigung (DE-588)4160648-6 s Frequenzbereichsdarstellung (DE-588)4199376-7 s 1\p DE-604 Chen, G. Sonstige oth Erscheint auch als Druck-Ausgabe 9789810226282 Erscheint auch als Druck-Ausgabe 9810226284 http://www.worldscientific.com/worldscibooks/10.1142/3070#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Moiola, Jorge L. Hopf bifurcation analysis a frequency domain approach Bifurcation theory Differential equations, Nonlinear / Numerical solutions Hopf-Verzweigung (DE-588)4160648-6 gnd Frequenzbereichsdarstellung (DE-588)4199376-7 gnd |
| subject_GND | (DE-588)4160648-6 (DE-588)4199376-7 |
| title | Hopf bifurcation analysis a frequency domain approach |
| title_auth | Hopf bifurcation analysis a frequency domain approach |
| title_exact_search | Hopf bifurcation analysis a frequency domain approach |
| title_full | Hopf bifurcation analysis a frequency domain approach Jorge L. Moiola, Guanrong Chen |
| title_fullStr | Hopf bifurcation analysis a frequency domain approach Jorge L. Moiola, Guanrong Chen |
| title_full_unstemmed | Hopf bifurcation analysis a frequency domain approach Jorge L. Moiola, Guanrong Chen |
| title_short | Hopf bifurcation analysis |
| title_sort | hopf bifurcation analysis a frequency domain approach |
| title_sub | a frequency domain approach |
| topic | Bifurcation theory Differential equations, Nonlinear / Numerical solutions Hopf-Verzweigung (DE-588)4160648-6 gnd Frequenzbereichsdarstellung (DE-588)4199376-7 gnd |
| topic_facet | Bifurcation theory Differential equations, Nonlinear / Numerical solutions Hopf-Verzweigung Frequenzbereichsdarstellung |
| url | http://www.worldscientific.com/worldscibooks/10.1142/3070#t=toc |
| work_keys_str_mv | AT moiolajorgel hopfbifurcationanalysisafrequencydomainapproach AT cheng hopfbifurcationanalysisafrequencydomainapproach |