Bifurcations in piecewise-smooth continuous systems:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2010
|
| Series: | World Scientific series on nonlinear science A
70 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 238 S. Ill., graph. Darst. |
| ISBN: | 9814293849 9789814293846 |
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Record in the Search Index
| _version_ | 1804145463325097984 |
|---|---|
| adam_text | Titel: Bifurcations in piecewise-smooth continuous systems
Autor: Simpson, David John Warwick
Jahr: 2010
Contents
Preface v
Acknowledgments xi
1. Fundamentals of Piecewise-Smooth, Continuous Systems 1
1.1 Applications.......................... 3
1.2 A Framework for Local Behavior.............. 8
1.3 Existence of Equilibria and Fixed Points.......... 12
1.4 The Observer Canonical Form................ 14
1.5 Discontinuous Bifurcations ................. 18
1.6 Border-Collision Bifurcations................ 20
1.7 Poincaré Maps and Discontinuity Maps .......... 24
1.8 Period Adding........................ 29
1.9 Smooth Approximations................... 31
2. Discontinuous Bifurcations in Planar Systems 33
2.1 Periodic Orbits........................ 34
2.2 The Focus-Focus Case in Detail............... 41
2.3 Summary and Classification................. 46
3. Codimension-Two, Discontinuous Bifurcations 53
3.1 A Nonsmooth, Saddle-Node Bifurcation.......... 56
3.2 A Nonsmooth, Hopf Bifurcation............... 59
3.3 A Codimension-Two, Discontinuous Hopf Bifurcation ... 70
4. The Growth of Saccharomyces cerevisiae 75
4.1 Mathematical Model..................... 77
xiv Bifurcations in Piecewise-Smooth, Continuous Systems
4.2 Basic Mathematical Observations.............. 82
4.3 Bifurcation Structure..................... 83
4.4 Simple and Complicated Stable Oscillations........ 89
5. Codimension-Two, Border-Collision Bifurcations 95
5.1 A Nonsmooth, Saddle-Node Bifurcation.......... 96
5.2 A Nonsmooth, Period-Doubling Bifurcation........ 99
6. Periodic Solutions and Resonance Tongues 107
6.1 Symbolic Dynamics...................... 109
6.2 Describing and Locating Periodic Solutions........ 112
6.3 Resonance Tongue Boundaries ............... 116
6.4 Rotational Symbol Sequences................ 122
6.5 Cardinality of Symbol Sequences.............. 125
6.6 Shrinking Points....................... 126
6.7 Unfolding Shrinking Points................. 131
7. Neimark-Sacker-Like Bifurcations 135
7.1 A Two-Dimensional Map .................. 137
7.2 Basic Dynamics........................ 139
7.3 Limiting Parameter Values ................. 142
7.4 Resonance Tongues...................... 145
7.5 Complex Phenomena Relating to Resonance Tongues . . . 153
7.6 More Complex Phenomena................. 160
Appendix A Selected Proofs 165
Lemma 1.3.............................. 165
Theorem 1.1............................. 166
Theorem 2.1............................. 167
Theorem 3.1............................. 171
Theorem 3.2............................. 173
Theorem 3.3............................ . 181
Theorem 3.4............................. 183
Theorem 5.2............................. 187
Theorem 5.3............................. 194
Lemma 6.9.............................. 197
Theorem 6.1............................. 199
Lemma 7.1.............................. 201
Contents xv
Appendix B Additional Figures 205
Appendix C Adjugate Matrices 211
Appendix D Parameter Values for S. cerevisiae 213
Bibliography 215
Index 237
|
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| id | DE-604.BV026833353 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:19:51Z |
| institution | BVB |
| isbn | 9814293849 9789814293846 |
| language | English |
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| physical | XV, 238 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific |
| record_format | marc |
| series | World Scientific series on nonlinear science A |
| series2 | World Scientific series on nonlinear science : Series A, Monographs and treatises |
| spelling | Simpson, David John Warwick Verfasser aut Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson Singapore [u.a.] World Scientific 2010 XV, 238 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier World Scientific series on nonlinear science : Series A, Monographs and treatises 70 Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s DE-604 World Scientific series on nonlinear science A 70 (DE-604)BV009051753 70 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022363231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simpson, David John Warwick Bifurcations in piecewise-smooth continuous systems World Scientific series on nonlinear science A Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4078889-1 |
| title | Bifurcations in piecewise-smooth continuous systems |
| title_auth | Bifurcations in piecewise-smooth continuous systems |
| title_exact_search | Bifurcations in piecewise-smooth continuous systems |
| title_full | Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson |
| title_fullStr | Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson |
| title_full_unstemmed | Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson |
| title_short | Bifurcations in piecewise-smooth continuous systems |
| title_sort | bifurcations in piecewise smooth continuous systems |
| topic | Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Verzweigung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022363231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009051753 |
| work_keys_str_mv | AT simpsondavidjohnwarwick bifurcationsinpiecewisesmoothcontinuoussystems |