Bifurcations: Sights, Sounds, and Mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Tokyo
Springer Japan
1993
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, however, should not be too simple, otherwise nothing interesting can happen. Albert Einstein once said "as simple as pos sible, but no more" . One of the major reasons for the circuits discussed being simple is due to their piecewise-linear characteristics. Namely, the voltage current relationships are composed of several line segments which are easy to build. Piecewise-linearity also simplifies rigorous analysis in a drastic man ner. (2) The piecewise-linearity of the circuits has far reaching consequences |
| Beschreibung: | 1 Online-Ressource (XVI, 468p. 138 illus) |
| ISBN: | 9784431682431 9784431682455 |
| DOI: | 10.1007/978-4-431-68243-1 |
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| 500 | |a Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, however, should not be too simple, otherwise nothing interesting can happen. Albert Einstein once said "as simple as pos sible, but no more" . One of the major reasons for the circuits discussed being simple is due to their piecewise-linear characteristics. Namely, the voltage current relationships are composed of several line segments which are easy to build. Piecewise-linearity also simplifies rigorous analysis in a drastic man ner. (2) The piecewise-linearity of the circuits has far reaching consequences | ||
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Datensatz im Suchindex
| _version_ | 1804153099559895040 |
|---|---|
| any_adam_object | |
| author | Matsumoto, Takashi |
| author_facet | Matsumoto, Takashi |
| author_role | aut |
| author_sort | Matsumoto, Takashi |
| author_variant | t m tm |
| building | Verbundindex |
| bvnumber | BV042423605 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184501954 (DE-599)BVBBV042423605 |
| dewey-full | 515.48 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.48 515.39 |
| dewey-search | 515.48 515.39 |
| dewey-sort | 3515.48 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-4-431-68243-1 |
| format | Electronic eBook |
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| isbn | 9784431682431 9784431682455 |
| language | English |
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| spelling | Matsumoto, Takashi Verfasser aut Bifurcations Sights, Sounds, and Mathematics by Takashi Matsumoto, Motomasa Komuro, Hiroshi Kokubu, Ryuji Tokunaga Tokyo Springer Japan 1993 1 Online-Ressource (XVI, 468p. 138 illus) txt rdacontent c rdamedia cr rdacarrier Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, however, should not be too simple, otherwise nothing interesting can happen. Albert Einstein once said "as simple as pos sible, but no more" . One of the major reasons for the circuits discussed being simple is due to their piecewise-linear characteristics. Namely, the voltage current relationships are composed of several line segments which are easy to build. Piecewise-linearity also simplifies rigorous analysis in a drastic man ner. (2) The piecewise-linearity of the circuits has far reaching consequences Mathematics Differentiable dynamical systems Systems theory Computer engineering Dynamical Systems and Ergodic Theory Systems Theory, Control Electrical Engineering Mathematik Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s 1\p DE-604 Chaostheorie (DE-588)4009754-7 s 2\p DE-604 Komuro, Motomasa Sonstige oth Kokubu, Hiroshi Sonstige oth Tokunaga, Ryuji Sonstige oth https://doi.org/10.1007/978-4-431-68243-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Matsumoto, Takashi Bifurcations Sights, Sounds, and Mathematics Mathematics Differentiable dynamical systems Systems theory Computer engineering Dynamical Systems and Ergodic Theory Systems Theory, Control Electrical Engineering Mathematik Verzweigung Mathematik (DE-588)4078889-1 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4078889-1 (DE-588)4009754-7 |
| title | Bifurcations Sights, Sounds, and Mathematics |
| title_auth | Bifurcations Sights, Sounds, and Mathematics |
| title_exact_search | Bifurcations Sights, Sounds, and Mathematics |
| title_full | Bifurcations Sights, Sounds, and Mathematics by Takashi Matsumoto, Motomasa Komuro, Hiroshi Kokubu, Ryuji Tokunaga |
| title_fullStr | Bifurcations Sights, Sounds, and Mathematics by Takashi Matsumoto, Motomasa Komuro, Hiroshi Kokubu, Ryuji Tokunaga |
| title_full_unstemmed | Bifurcations Sights, Sounds, and Mathematics by Takashi Matsumoto, Motomasa Komuro, Hiroshi Kokubu, Ryuji Tokunaga |
| title_short | Bifurcations |
| title_sort | bifurcations sights sounds and mathematics |
| title_sub | Sights, Sounds, and Mathematics |
| topic | Mathematics Differentiable dynamical systems Systems theory Computer engineering Dynamical Systems and Ergodic Theory Systems Theory, Control Electrical Engineering Mathematik Verzweigung Mathematik (DE-588)4078889-1 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | Mathematics Differentiable dynamical systems Systems theory Computer engineering Dynamical Systems and Ergodic Theory Systems Theory, Control Electrical Engineering Mathematik Verzweigung Mathematik Chaostheorie |
| url | https://doi.org/10.1007/978-4-431-68243-1 |
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