Periodic motions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1994
|
| Schriftenreihe: | Applied mathematical sciences
104 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 577 S. graph. Darst. |
| ISBN: | 3540942041 0387942041 |
Internformat
MARC
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| 100 | 1 | |a Farkas, Miklós |d 1932- |e Verfasser |0 (DE-588)113735308 |4 aut | |
| 245 | 1 | 0 | |a Periodic motions |c Miklós Farkas |
| 264 | 1 | |a New York u.a. |b Springer |c 1994 | |
| 300 | |a XIII, 577 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 104 | |
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| 650 | 7 | |a Equations différentielles - Solutions numériques |2 ram | |
| 650 | 7 | |a Numerieke methoden |2 gtt | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
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| 650 | 0 | 7 | |a Periodische Lösung |0 (DE-588)4199269-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804123952070524928 |
|---|---|
| adam_text | Contents
Preface vii
1 Introduction 1
1.1 Existence, Uniqueness and Analytic Properties of Solutions 2
1.2 Linear Systems 10
1.3 Dynamical Systems 16
1.4 Stability 20
1.5 Liapunov s Direct Method 33
1.6 Problems 42
2 Periodic Solutions of Linear Systems 45
2.1 Linear Systems with Constant Coefficients 45
2.2 Homogeneous Linear Systems with Periodic Coefficients . . 52
2.3 Forced Linear Oscillations 60
2.4 Stability of Linear Systems 66
2.5 Hill s and Mathieu s Equations 71
2.6 Problems 82
3 Autonomous Systems in the Plane 83
3.1 The Poincare Bendixson Theory 84
3.2 Lienard s Equation 97
3.3 Duffing s Equation 108
3.4 The Lotka Volterra Predator Prey Model and
Generalizations 114
xii Contents
3.5 The Poincare Index and Non existence of Cycles 122
3.6 Hilbert s Sixteenth Problem 141
3.7 Problems 149
4 Periodic Solutions of Periodic Systems 151
4.1 Existence of Periodic Solutions 152
4.2 Stability and Isolation of Periodic Solutions 161
4.3 Periodically Forced Lienard and Duffing Equations 171
4.4 Two Competing Species in a Periodically Changing
Environment 183
4.5 Applications in Higher Dimensions 194
4.6 Problems 202
5 Autonomous Systems of Arbitrary Dimension 205
5.1 Orbital Stability 206
5.2 Poincare Map, Isolation and Isochronism 219
5.3 D periodic Solutions of Cylindrical Systems 234
5.4 Existence of Periodic Solutions 250
5.5 Competitive and Cooperative Systems,
Existence in Dimension Three 274
5.6 Invariant and Integral Manifolds of Periodic Solutions . . . 290
5.7 Problems 299
6 Perturbations 301
6.1 Periodic Perturbations of Periodic Systems 302
6.2 Controllably Periodic Perturbations of
Autonomous Systems 314
6.3 The Stability of Perturbed Periodic Solutions 341
6.4 Controllably Periodic Perturbations of
Van der Pol s Equation 353
6.5 Averaging 361
6.6 Singular Perturbations and Relaxation Oscillations 371
6.7 Aperiodic Perturbations 381
6.8 Problems 396
7 Bifurcations 399
7.1 Structural Stability and Bifurcations 400
7.2 The Andronov Hopf Bifurcation 411
7.3 A Predator Prey Model with Memory 439
7.4 Zip Bifurcation in Competitive Systems 457
7.5 Functional Differential Equations 476
7.6 Through Periodic Motions to Chaos 491
7.7 Problems 501
Contents xiii
Appendix 503
Al Matrices 503
A2 Topological Degree and Fixed Point Theorems 519
A3 Invariant Manifolds 531
References 545
Symbols 569
Index 571
|
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| author | Farkas, Miklós 1932- |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV009610621 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:37:56Z |
| institution | BVB |
| isbn | 3540942041 0387942041 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006352947 |
| oclc_num | 29667938 |
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| physical | XIII, 577 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Farkas, Miklós 1932- Verfasser (DE-588)113735308 aut Periodic motions Miklós Farkas New York u.a. Springer 1994 XIII, 577 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 104 Differentiaalvergelijkingen gtt Equations différentielles - Solutions numériques ram Numerieke methoden gtt Differential equations Numerical solutions Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Periodische Lösung (DE-588)4199269-6 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Periodische Lösung (DE-588)4199269-6 s Applied mathematical sciences 104 (DE-604)BV000005274 104 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006352947&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farkas, Miklós 1932- Periodic motions Applied mathematical sciences Differentiaalvergelijkingen gtt Equations différentielles - Solutions numériques ram Numerieke methoden gtt Differential equations Numerical solutions Differentialgleichung (DE-588)4012249-9 gnd Periodische Lösung (DE-588)4199269-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4199269-6 (DE-588)4128130-5 (DE-588)4020929-5 |
| title | Periodic motions |
| title_auth | Periodic motions |
| title_exact_search | Periodic motions |
| title_full | Periodic motions Miklós Farkas |
| title_fullStr | Periodic motions Miklós Farkas |
| title_full_unstemmed | Periodic motions Miklós Farkas |
| title_short | Periodic motions |
| title_sort | periodic motions |
| topic | Differentiaalvergelijkingen gtt Equations différentielles - Solutions numériques ram Numerieke methoden gtt Differential equations Numerical solutions Differentialgleichung (DE-588)4012249-9 gnd Periodische Lösung (DE-588)4199269-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differentiaalvergelijkingen Equations différentielles - Solutions numériques Numerieke methoden Differential equations Numerical solutions Differentialgleichung Periodische Lösung Numerisches Verfahren Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006352947&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT farkasmiklos periodicmotions |