Applied nonlinear dynamics: analytical, computational, and experimental methods
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Weinheim [u.a.]
Wiley-VCH
2004
|
| Schriftenreihe: | Wiley series in nonlinear science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 685 S. Ill. Ill., graph. Darst. |
| ISBN: | 0471593486 9780471593485 |
Internformat
MARC
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| 020 | |a 0471593486 |9 0-471-59348-6 | ||
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| 084 | |a MAT 344f |2 stub | ||
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| 100 | 1 | |a Nayfeh, Ali Hasan |d 1933-2017 |e Verfasser |0 (DE-588)151240388 |4 aut | |
| 245 | 1 | 0 | |a Applied nonlinear dynamics |b analytical, computational, and experimental methods |c Ali H. Nayfeh ; Balakumar Balachandran |
| 264 | 1 | |a Weinheim [u.a.] |b Wiley-VCH |c 2004 | |
| 300 | |a XV, 685 S. Ill. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in nonlinear science | |
| 650 | 0 | 7 | |a Nichtlineare Dynamik |0 (DE-588)4126141-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Dynamik |0 (DE-588)4126141-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Balachandran, Balakumar |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016482749&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016482749 | ||
Datensatz im Suchindex
| _version_ | 1804137625139806208 |
|---|---|
| adam_text | CONTENTS
PREFACE
xiii
1
INTRODUCTION
1
Li DISCRETE-TÏME
SYSTEMS
............... 2
1.2
CONTINUOUS-TIME
SYSTEMS
............ 6
1.2.1
Nonautonomous Systems
.............. 6
1.2.2
Autonomous
Systems
................ 11
1.2.3
Phase Portraits
and Flows
............. 13
1.3
ATTRACTING SETS
................... 15
1.4
CONCEPTS
OF STABILITY
............... 20
1.4.1
Lyapunov Stability
................. 20
1.4.2
Asymptotic Stability
................ 23
1.4.3
Poincaré
Stability
.................. 25
1.4.4 Lagrange
Stability (Bounded Stability)
...... 27
1.4.5
Stability Through Lyapunov Function
....... 27
1.5
ATTRACTORS
....................... 29
1.6
COMMENTS
........................ 31
1.7
EXERCISES
........................ 31
2
EQUILIBRIUM SOLUTIONS
35
2.1
CONTINUOUS-TIME SYSTEMS
............ 35
2.1.1
Linearization Near an Equilibrium Solution
... 36
2.1.2
Classification and Stability of Equilibrium Solu¬
tions
......................... 39
2-1.3 Eigenspaces
and Invariant Manifolds
....... 47
2.1.4
Analytical Construction of Stable and Unstable
Manifolds
...................... 58
vii
viii CONTENTS
2.2
FIXED POINTS OF MAPS
................61
2.3
BIFURCATIONS OF CONTINUOUS SYSTEMS
.... 68
2.3.1
Local Bifurcations of Fixed Points
.........70
2.3.2
Normal Forms for Bifurcations
...........81
2.3.3
Bifurcation Diagrams and Sets
...........83
2.3.4
Center Manifold Reduction
............96
2.3.5
The Lyapunov-Schmidt Method
..........108
2.3.6
The Method of Multiple Scales
..........108
2.3.7
Structural Stability
.................115
2.3.8
Stability of Bifurcations to Perturbations
.....116
2.3.9
Codimension of a Bifurcation
...........119
2.3.10
Global Bifurcations
.................121
2.4
BIFURCATIONS OF MAPS
................121
2.5
EXERCISES
........................128
3
PERIODIC SOLUTIONS
147
3.1
PERIODIC SOLUTIONS
.................147
3.1.1
Autonomous Systems
................148
3.1.2
Nonautonomous Systems
..............156
3.1.3
Comments
......................158
3.2
FLOQUET THEORY
...................158
3.2.1
Autonomous Systems
................159
3.2.2
Nonautonomous Systems
..............169
3.2.3
Comments on the Monodromy Matrix
......171
3.2.4
Manifolds of a Periodic Solution
..........172
3.3
POINCARÉ
MAPS
.....................172
3.3.1
Nonautonomous Systems
..............176
3.3.2
Autonomous Systems
................181
3.4
BIFURCATIONS
......................187
3.4.1
Symmetry-Breaking Bifurcation
..........189
3.4.2
Cyclic-Fold Bifurcation
...............195
3.4.3
Period-Doubling or Flip Bifurcation
.......200
3.4.4
Transcritical Bifurcation
..............204
3.4.5
Secondary
Hopf
or Neimark Bifurcation
......205
3.5
ANALYTICAL CONSTRUCTIONS
...........208
3.5.1
Method of Multiple Scales
.............209
3.5.2
Center Manifold Reduction
............212
CONTENTS ix
3.5.3 General
Case....................
217
3.6
EXERCISES
........................219
4 QUASIPEBIOpiC SOLUTIONS 231
4.1
POINCARÉ
MAPS
.....................233
4.1.1
Winding Time and Rotation Number
.......238
4.1.2
Second-Order
Poincaré Map
............240
4.1.3
Comments
......................241
4.2
CIRCLE MAP
.......................242
4.3
CONSTRUCTIONS
....................248
4.3.1
Method of Multiple
Scalee
.............249
4.3.2
Spectral Balance Method
..............251
4.3.3
Poincaré Map
Method
...............253
4.4
STABILITY
.........................254
4.5
SYNCHRONIZATION
...................255
4.6
EXERCISES
........................269
Ï
CHAOS
277
5.1
MAPS
............................278
5.2
CONTINUOUS-TIME SYSTEMS
............288
5.3
PERIOD-DOUBLING SCENARIO
............295
5.4
INTERMITTENCY MECHANISMS
...........296
5.4.1
Type I Intermittency
................300
5.4.2
Type III Intermittency
...............305
5.4.3
Type II Intermittency
...............311
5.5
QUASIPERIODIC ROUTES
...............314
5.5.1
Ruelle-Takens Scenario
...............315
5.5.2
Torus Breakdown
..................317
5.5.3
Torus Doubling
...................331
5.6
CRISES
...........................334
5.7
MELNIKOV THEORY
...................356
5.7.1
Homoclinic Tangles
.................356
5.7.2
Heteroclinic Tangles
................359
5.7.3
Numerical Prediction of Manifold Intersections
. . 363
5.7.4
Analytical Prediction of Manifold Intersections
. . 366
5.7.5
Application of Melnikov s Method
.........374
5.7.6
Comments
.....................390
χ
CONTENTS
5.8
BIFURCATIONS
OF HOMOCLINIC ORBITS
.....390
5.8.1
Planar Systems
...................391
5.8.2
Orbits Homoclinic to a Saddle
...........397
5.8.3
Orbits Homoclinic to a Saddle Focus
.......402
5.8.4
Comments
......................407
5.9
EXERCISES
........................410
6
NUMERICAL METHODS
423
6.1
CONTINUATION OF FIXED POINTS
.........423
6.1.1
Sequential Continuation
..............425
6.1.2
Davidenko-Newton-Raphson Continuation
.... 428
6.1.3
Arclength Continuation
..............428
6.1.4
Pseudo-Arclength Continuation
..........432
6.1.5
Comments
......................435
6.2
SIMPLE TURNING AND BRANCH POINTS
......436
6.3 HOPF
BIFURCATION POINTS
.............438
6.4
HOMOTOPY ALGORITHMS
...............441
6.5
CONSTRUCTION OF PERIODIC SOLUTIONS
.... 445
6.5.1
Finite-Difference Method
.............446
6.5.2
Shooting Method
..................449
6.5.3
Poincaré
Map Method
...............455
6.6
CONTINUATION OF PERIODIC SOLUTIONS
.... 455
6.6.1
Sequential Continuation
..............456
6.6.2
Arclength Continuation
..............456
6.6.3
Pseudo-Arclength Continuation
..........458
6.6.4
Comments
......................460
7
TOOLS TO ANALYZE MOTIONS
461
7.1
INTRODUCTION
.....................462
7.2
TIME HISTORIES
.....................465
7.3
STATE SPACE
.......................472
7.4
PSEUDO-STATE SPACE
.................478
7.4.1
Choosing the Embedding Dimension
.......483
7.4.2
Choosing the Time Delay
.............495
7.4.3
Two or More Measured Signals
..........500
7.5
FOURIER SPECTRA
...................502
7.6
POINCARÉ
SECTIONS AND MAPS
..........514
CONTENTS xi
7.6.1 Systems
of
Equations
................514
7.6.2 Experiments.....................516
7.6.3
Higher-Order
Poincaré Sections
..........519
7.6.4
Comments......................
519
7.7
AUTOCORRELATION
FUNCTIONS..........
520
7.8
LYAPUNOV EXPONENTS
................525
7.8.1
Concept of Lyapunov Exponents
.........525
7.8.2
Autonomous Systems
................529
7.8.3
Maps
.........................531
7.8.4
Reconstructed Space
................534
7.8.5
Comments
......................537
7.9
DIMENSION CALCULATIONS
..............538
7.9.1
Capacity Dimension
................538
7.9.2
Pointwise Dimension
................541
7.9.3
Information Dimension
...............545
7.9.4
Correlation Dimension
...............547
7.9.5
Generalized Correlation Dimension
........548
7.9.6
Lyapunov Dimension
................549
7.9.7
Comments
......................549
7.10
HIGHER-ORDER SPECTRA
...............550
7.11
EXERCISES
........................557
8
CONTROL
563
8.1
CONTROL OF BIFURCATIONS
.............563
8.1.1
Static Feedback Control
..............564
8.1.2
Dynamic Feedback Control
.............568
8.1.3
Comments
......................571
8.2
CHAOS CONTROL
....................571
8.2.1
The OGY Scheme
..................572
8.2.2
Implementation of the OGY Scheme
.......577
8.2.3
Pole Placement Technique
.............580
8.2.4
Traditional Control Methods
............582
8.3
SYNCHRONIZATION
...................584
BIBLIOGRAPHY
589
SUBJECT INDEX
663
|
| adam_txt |
CONTENTS
PREFACE
xiii
1
INTRODUCTION
1
Li DISCRETE-TÏME
SYSTEMS
. 2
1.2
CONTINUOUS-TIME
SYSTEMS
. 6
1.2.1
Nonautonomous Systems
. 6
1.2.2
Autonomous
Systems
. 11
1.2.3
Phase Portraits
and Flows
. 13
1.3
ATTRACTING SETS
. 15
1.4
CONCEPTS
OF STABILITY
. 20
1.4.1
Lyapunov Stability
. 20
1.4.2
Asymptotic Stability
. 23
1.4.3
Poincaré
Stability
. 25
1.4.4 Lagrange
Stability (Bounded Stability)
. 27
1.4.5
Stability Through Lyapunov Function
. 27
1.5
ATTRACTORS
. 29
1.6
COMMENTS
. 31
1.7
EXERCISES
. 31
2
EQUILIBRIUM SOLUTIONS
35
2.1
CONTINUOUS-TIME SYSTEMS
. 35
2.1.1
Linearization Near an Equilibrium Solution
. 36
2.1.2
Classification and Stability of Equilibrium Solu¬
tions
. 39
2-1.3 Eigenspaces
and Invariant Manifolds
. 47
2.1.4
Analytical Construction of Stable and Unstable
Manifolds
. 58
vii
viii CONTENTS
2.2
FIXED POINTS OF MAPS
.61
2.3
BIFURCATIONS OF CONTINUOUS SYSTEMS
. 68
2.3.1
Local Bifurcations of Fixed Points
.70
2.3.2
Normal Forms for Bifurcations
.81
2.3.3
Bifurcation Diagrams and Sets
.83
2.3.4
Center Manifold Reduction
.96
2.3.5
The Lyapunov-Schmidt Method
.108
2.3.6
The Method of Multiple Scales
.108
2.3.7
Structural Stability
.115
2.3.8
Stability of Bifurcations to Perturbations
.116
2.3.9
Codimension of a Bifurcation
.119
2.3.10
Global Bifurcations
.121
2.4
BIFURCATIONS OF MAPS
.121
2.5
EXERCISES
.128
3
PERIODIC SOLUTIONS
147
3.1
PERIODIC SOLUTIONS
.147
3.1.1
Autonomous Systems
.148
3.1.2
Nonautonomous Systems
.156
3.1.3
Comments
.158
3.2
FLOQUET THEORY
.158
3.2.1
Autonomous Systems
.159
3.2.2
Nonautonomous Systems
.169
3.2.3
Comments on the Monodromy Matrix
.171
3.2.4
Manifolds of a Periodic Solution
.172
3.3
POINCARÉ
MAPS
.172
3.3.1
Nonautonomous Systems
.176
3.3.2
Autonomous Systems
.181
3.4
BIFURCATIONS
.187
3.4.1
Symmetry-Breaking Bifurcation
.189
3.4.2
Cyclic-Fold Bifurcation
.195
3.4.3
Period-Doubling or Flip Bifurcation
.200
3.4.4
Transcritical Bifurcation
.204
3.4.5
Secondary
Hopf
or Neimark Bifurcation
.205
3.5
ANALYTICAL CONSTRUCTIONS
.208
3.5.1
Method of Multiple Scales
.209
3.5.2
Center Manifold Reduction
.212
CONTENTS ix
3.5.3 General
Case.
217
3.6
EXERCISES
.219
4 QUASIPEBIOpiC SOLUTIONS 231
4.1
POINCARÉ
MAPS
.233
4.1.1
Winding Time and Rotation Number
.238
4.1.2
Second-Order
Poincaré Map
.240
4.1.3
Comments
.241
4.2
CIRCLE MAP
.242
4.3
CONSTRUCTIONS
.248
4.3.1
Method of Multiple
Scalee
.249
4.3.2
Spectral Balance Method
.251
4.3.3
Poincaré Map
Method
.253
4.4
STABILITY
.254
4.5
SYNCHRONIZATION
.255
4.6
EXERCISES
.269
Ï
CHAOS
277
5.1
MAPS
.278
5.2
CONTINUOUS-TIME SYSTEMS
.288
5.3
PERIOD-DOUBLING SCENARIO
.295
5.4
INTERMITTENCY MECHANISMS
.296
5.4.1
Type I Intermittency
.300
5.4.2
Type III Intermittency
.305
5.4.3
Type II Intermittency
.311
5.5
QUASIPERIODIC ROUTES
.314
5.5.1
Ruelle-Takens Scenario
.315
5.5.2
Torus Breakdown
.317
5.5.3
Torus Doubling
.331
5.6
CRISES
.334
5.7
MELNIKOV THEORY
.356
5.7.1
Homoclinic Tangles
.356
5.7.2
Heteroclinic Tangles
.359
5.7.3
Numerical Prediction of Manifold Intersections
. . 363
5.7.4
Analytical Prediction of Manifold Intersections
. . 366
5.7.5
Application of Melnikov's Method
.374
5.7.6
Comments
.390
χ
CONTENTS
5.8
BIFURCATIONS
OF HOMOCLINIC ORBITS
.390
5.8.1
Planar Systems
.391
5.8.2
Orbits Homoclinic to a Saddle
.397
5.8.3
Orbits Homoclinic to a Saddle Focus
.402
5.8.4
Comments
.407
5.9
EXERCISES
.410
6
NUMERICAL METHODS
423
6.1
CONTINUATION OF FIXED POINTS
.423
6.1.1
Sequential Continuation
.425
6.1.2
Davidenko-Newton-Raphson Continuation
. 428
6.1.3
Arclength Continuation
.428
6.1.4
Pseudo-Arclength Continuation
.432
6.1.5
Comments
.435
6.2
SIMPLE TURNING AND BRANCH POINTS
.436
6.3 HOPF
BIFURCATION POINTS
.438
6.4
HOMOTOPY ALGORITHMS
.441
6.5
CONSTRUCTION OF PERIODIC SOLUTIONS
. 445
6.5.1
Finite-Difference Method
.446
6.5.2
Shooting Method
.449
6.5.3
Poincaré
Map Method
.455
6.6
CONTINUATION OF PERIODIC SOLUTIONS
. 455
6.6.1
Sequential Continuation
.456
6.6.2
Arclength Continuation
.456
6.6.3
Pseudo-Arclength Continuation
.458
6.6.4
Comments
.460
7
TOOLS TO ANALYZE MOTIONS
461
7.1
INTRODUCTION
.462
7.2
TIME HISTORIES
.465
7.3
STATE SPACE
.472
7.4
PSEUDO-STATE SPACE
.478
7.4.1
Choosing the Embedding Dimension
.483
7.4.2
Choosing the Time Delay
.495
7.4.3
Two or More Measured Signals
.500
7.5
FOURIER SPECTRA
.502
7.6
POINCARÉ
SECTIONS AND MAPS
.514
CONTENTS xi
7.6.1 Systems
of
Equations
.514
7.6.2 Experiments.516
7.6.3
Higher-Order
Poincaré Sections
.519
7.6.4
Comments.
519
7.7
AUTOCORRELATION
FUNCTIONS.
520
7.8
LYAPUNOV EXPONENTS
.525
7.8.1
Concept of Lyapunov Exponents
.525
7.8.2
Autonomous Systems
.529
7.8.3
Maps
.531
7.8.4
Reconstructed Space
.534
7.8.5
Comments
.537
7.9
DIMENSION CALCULATIONS
.538
7.9.1
Capacity Dimension
.538
7.9.2
Pointwise Dimension
.541
7.9.3
Information Dimension
.545
7.9.4
Correlation Dimension
.547
7.9.5
Generalized Correlation Dimension
.548
7.9.6
Lyapunov Dimension
.549
7.9.7
Comments
.549
7.10
HIGHER-ORDER SPECTRA
.550
7.11
EXERCISES
.557
8
CONTROL
563
8.1
CONTROL OF BIFURCATIONS
.563
8.1.1
Static Feedback Control
.564
8.1.2
Dynamic Feedback Control
.568
8.1.3
Comments
.571
8.2
CHAOS CONTROL
.571
8.2.1
The OGY Scheme
.572
8.2.2
Implementation of the OGY Scheme
.577
8.2.3
Pole Placement Technique
.580
8.2.4
Traditional Control Methods
.582
8.3
SYNCHRONIZATION
.584
BIBLIOGRAPHY
589
SUBJECT INDEX
663 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Nayfeh, Ali Hasan 1933-2017 Balachandran, Balakumar |
| author_GND | (DE-588)151240388 |
| author_facet | Nayfeh, Ali Hasan 1933-2017 Balachandran, Balakumar |
| author_role | aut aut |
| author_sort | Nayfeh, Ali Hasan 1933-2017 |
| author_variant | a h n ah ahn b b bb |
| building | Verbundindex |
| bvnumber | BV023298253 |
| classification_rvk | SK 810 |
| classification_tum | MAT 344f MAT 354f |
| ctrlnum | (OCoLC)315832878 (DE-599)BVBBV023298253 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV023298253 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:45:32Z |
| indexdate | 2024-07-09T21:15:16Z |
| institution | BVB |
| isbn | 0471593486 9780471593485 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016482749 |
| oclc_num | 315832878 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-11 |
| physical | XV, 685 S. Ill. Ill., graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Wiley-VCH |
| record_format | marc |
| series2 | Wiley series in nonlinear science |
| spelling | Nayfeh, Ali Hasan 1933-2017 Verfasser (DE-588)151240388 aut Applied nonlinear dynamics analytical, computational, and experimental methods Ali H. Nayfeh ; Balakumar Balachandran Weinheim [u.a.] Wiley-VCH 2004 XV, 685 S. Ill. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in nonlinear science Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s DE-604 Balachandran, Balakumar Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016482749&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nayfeh, Ali Hasan 1933-2017 Balachandran, Balakumar Applied nonlinear dynamics analytical, computational, and experimental methods Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| subject_GND | (DE-588)4126141-0 |
| title | Applied nonlinear dynamics analytical, computational, and experimental methods |
| title_auth | Applied nonlinear dynamics analytical, computational, and experimental methods |
| title_exact_search | Applied nonlinear dynamics analytical, computational, and experimental methods |
| title_exact_search_txtP | Applied nonlinear dynamics analytical, computational, and experimental methods |
| title_full | Applied nonlinear dynamics analytical, computational, and experimental methods Ali H. Nayfeh ; Balakumar Balachandran |
| title_fullStr | Applied nonlinear dynamics analytical, computational, and experimental methods Ali H. Nayfeh ; Balakumar Balachandran |
| title_full_unstemmed | Applied nonlinear dynamics analytical, computational, and experimental methods Ali H. Nayfeh ; Balakumar Balachandran |
| title_short | Applied nonlinear dynamics |
| title_sort | applied nonlinear dynamics analytical computational and experimental methods |
| title_sub | analytical, computational, and experimental methods |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| topic_facet | Nichtlineare Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016482749&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nayfehalihasan appliednonlineardynamicsanalyticalcomputationalandexperimentalmethods AT balachandranbalakumar appliednonlineardynamicsanalyticalcomputationalandexperimentalmethods |