Dynamical systems with applications using Mathematica:
"The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering, Many chapters of the book are especially useful as reference material for senior undergraduate independent project work."--BOOK...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, Mass. [u.a.]
Birkhäuser
2007
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering, Many chapters of the book are especially useful as reference material for senior undergraduate independent project work."--BOOK JACKET. |
| Beschreibung: | Literaturverz. S. [451] - 468 |
| Beschreibung: | XV, 484 S. graph. Darst. |
| ISBN: | 9780817644826 |
Internformat
MARC
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| 100 | 1 | |a Lynch, Stephen |d 1964- |e Verfasser |0 (DE-588)122765052 |4 aut | |
| 245 | 1 | 0 | |a Dynamical systems with applications using Mathematica |c Stephen Lynch |
| 264 | 1 | |a Boston, Mass. [u.a.] |b Birkhäuser |c 2007 | |
| 300 | |a XV, 484 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. [451] - 468 | ||
| 520 | 1 | |a "The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering, Many chapters of the book are especially useful as reference material for senior undergraduate independent project work."--BOOK JACKET. | |
| 630 | 0 | 4 | |a Mathematica (Computer file) |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Differential dynamical systems |x Data processing | |
| 650 | 0 | 7 | |a Mathematica |g Programm |0 (DE-588)4268208-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematica 11.3 |0 (DE-588)1173190325 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016272410 | ||
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| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804137311608242176 |
|---|---|
| adam_text | Contents
Preface
xi
0
A
Tutorial
Introduction to
Mathematica
1
0.1
A Quick Tour of
Mathematica
................... 2
0.2
Tutorial One: The Basics (One Hour)
............... 4
0.3
Tutorial Two: Plots and Differential Equations (One Hour)
... 6
0.4
The Manipulate Command and Simple
Mathematica
Programs
. 8
0.5
Hints for Programming
...................... 11
0.6
Mathematica
Exercises
...................... 12
1
Differential Equations
17
1.1
Simple Differential Equations and Applications
......... 18
1.2
Applications to Chemical Kinetics
................ 25
1.3
Applications to Electric Circuits
................. 29
1.4
Existence and Uniqueness Theorem
................ 32
1.5
Mathematica
Commands in Text Format
............. 35
1.6
Exercises
.............................. 36
2
Planar Systems
41
2.1
Canonical Forms
......................... 42
2.2
Eigenvectors Defining Stable and Unstable Manifolds
...... 46
2.3
Phase Portraits of Linear Systems in the Plane
.......... 49
vi
Contents
2.4
Linearization and Hartman s Theorem
.............. 54
2.5
Constructing Phase Plane Diagrams
............... 55
2.6
Mathematica
Commands in Text Format
............. 64
2.7
Exercises
.............................. 65
3
Interacting Species
69
3.1
Competing Species
........................ 69
3.2
Predator-Prey Models
....................... 72
3.3
Other Characteristics Affecting Interacting Species
....... 78
3.4
Mathematica
Commands in Text Format
............. 80
3.5
Exercises
.............................. 81
4
Limit Cycles
85
4.1
Historical Background
....................... 86
4.2
Existence and Uniqueness of Limit Cycles in the Plane
..... 89
4.3
Nonexistence of Limit Cycles in the Plane
............ 95
4.4
Perturbation Methods
....................... 98
4.5
Mathematica
Commands in Text Format
............. 106
4.6
Exercises
.............................. 107
5
Hamiltonian Systems, Lyapunov Functions, and Stability 111
5.1
Hamiltonian Systems in the Plane
................. 112
5.2
Lyapunov Functions and Stability
................. 117
5.3
Mathematica
Commands in Text Format
............. 122
5.4
Exercises
.............................. 123
6
Bifurcation Theory
127
6.1
Bifurcations of Nonlinear Systems in the Plane
.......... 128
6.2
Normal Forms
........................... 134
6.3
Multistability and Bistability
................... 137
6.4
Mathematica
Commands in Text Format
............. 140
6.5
Exercises
.............................. 140
7
Three-Dimensional Autonomous Systems and Chaos
145
7.1
Linear Systems and Canonical Forms
............... 146
7.2
Nonlinear Systems and Stability
................. 150
7.3
The
Rössler
System and Chaos
.................. 154
7.4
The
Lorenz
Equations, Chua s Circuit, and the
Belousov-Zhabotinski Reaction
................. 158
7.5
Mathematica
Commands in Text Format
............. 165
7.6
Exercises
.............................. 166
8
Poincaré
Maps and Nonautonomous Systems in the Plane
171
8.1
Poincaré
Maps
........................... 172
Contents
vii
8.2 Hamiltonian Systems
with Two Degrees of Freedom
....... 178
8.3
Nonautonomous Systems in the Plane
.............. 181
8.4
Mathematica
Commands in Text Format
............. 189
8.5
Exercises
.............................. 192
9
Local and Global Bifurcations
195
9.1
Small-Amplitude Limit Cycle Bifurcations
............ 196
9.2 Gröbner
Bases
........................... 201
9.3
Melnikov Integrals and Bifurcating Limit Cycles from a
Center
............................... 207
9.4
Bifurcations Involving Homoclinic Loops
............ 209
9.5
Mathematica
Commands in Text Format
............. 211
9.6
Exercises
.............................. 213
10
The Second Part of Hilbert s Sixteenth Problem
217
10.1
Statement of Problem and Main Results
............. 218
10.2
Poincaré Compactification
.................... 220
10.3
Global Results for
Liénard
Systems
................ 227
10.4
Local Results for
Liénard
Systems
................ 235
10.5
Exercises
.............................. 237
11
Linear Discrete Dynamical Systems
241
11.1
Recurrence Relations
....................... 242
11.2
The Leslie Model
......................... 247
11.3
Harvesting and Culling Policies
.................. 251
11.4
Mathematica
Commands in Text Format
............. 255
11.5
Exercises
.............................. 256
12
Nonlinear Discrete Dynamical Systems
261
12.1
The Tent Map and Graphical Iterations
.............. 262
12.2
Fixed Points and Periodic Orbits
................. 266
12.3
The Logistic Map, Bifurcation Diagram, and
Feigenbaum
Number
.............................. 273
12.4
Gaussian and
Hénon
Maps
.................... 281
12.5
Applications
............................ 285
12.6
Mathematica
Commands in Text Format
............. 288
12.7
Exercises
.............................. 289
13
Complex Iterative Maps
293
13.1
Julia Sets and the Mandelbrot Set
................. 294
13.2
Boundaries of Periodic Orbits
................... 298
13.3
Mathematica
Commands in Text Format
............. 300
13.4
Exercises
.............................. 302
viii Contents
14
Electromagnetic
Waves and Optical Resonators
305
14.1
Maxwell s Equations and Electromagnetic Waves
........306
14.2
Historical Background
.......................308
14.3
The Nonlinear
SFR
Resonator
..................312
14.4
Chaotic Attractors and Bistability
.................314
14.5
Linear Stability Analysis
.....................318
14.6
Instabilities and Bistability
....................321
14.7
Mathematica
Commands in Text Format
.............325
14.8
Exercises
..............................327
15
Fractals and
Multirraciais
331
15.1
Construction of Simple Examples
.................332
15.2
Calculating Fractal Dimensions
..................338
15.3
A Multifractal Formalism
.....................343
15.4
Multirraciais
in the Real World and Some Simple Examples
. . . 348
15.5
Mathematica
Commands in Text Format
.............356
15.6
Exercises
..............................357
16
Chaos Control and Synchronization
363
16.1
Historical Background
.......................364
16.2
Controlling Chaos in the Logistic Map
..............368
16.3
Controlling Chaos in the
Hénon
Map
...............372
16.4
Chaos Synchronization
......................376
16.5
Mathematica
Commands in Text Format
.............379
16.6
Exercises
..............................381
17
Neural Networks
387
17.1
Introduction
............................388
17.2
The Delta Learning Rule and Backpropagation
..........394
17.3
The Hopfield Network and Lyapunov Stability
..........398
17.4
Neurodynamics
..........................408
17.5
Mathematica
Commands in Text Format
.............411
17.6
Exercises
..............................415
18
Examination-Type Questions
421
18.1
Dynamical Systems with Applications
..............421
18.2
Dynamical Systems with
Mathematica
..............424
19
Solutions to Exercises
429
19.0
Chapter
0 .............................429
19.1
Chapter
1 .............................431
19.2
Chapter
2 .............................431
19.3
Chapters
.............................433
19.4
Chapter
4 .............................435
Contents ix
19.5
Chapter
5 ............................. 436
19.6
Chapter
6 ............................. 437
19.7
Chapter?
............................. 438
19.8
Chapter
8 ............................. 439
19.9
Chapter
9 ............................. 440
19.10
Chapter
10............................. 440
19.11
Chapter
11............................. 442
19.12
Chapter
12............................. 444
19.13
Chapter
13............................. 445
19.14
Chapter
14............................. 446
19.15
Chapter
15............................. 446
19.16
Chapter
16............................. 447
19.17
Chapter
17............................. 447
19.18
Chapter
18............................. 448
References
451
Textbooks
.................................451
Research Papers
..............................459
Mathematica
Program Index
469
Index
473
|
| adam_txt |
Contents
Preface
xi
0
A
Tutorial
Introduction to
Mathematica
1
0.1
A Quick Tour of
Mathematica
. 2
0.2
Tutorial One: The Basics (One Hour)
. 4
0.3
Tutorial Two: Plots and Differential Equations (One Hour)
. 6
0.4
The Manipulate Command and Simple
Mathematica
Programs
. 8
0.5
Hints for Programming
. 11
0.6
Mathematica
Exercises
. 12
1
Differential Equations
17
1.1
Simple Differential Equations and Applications
. 18
1.2
Applications to Chemical Kinetics
. 25
1.3
Applications to Electric Circuits
. 29
1.4
Existence and Uniqueness Theorem
. 32
1.5
Mathematica
Commands in Text Format
. 35
1.6
Exercises
. 36
2
Planar Systems
41
2.1
Canonical Forms
. 42
2.2
Eigenvectors Defining Stable and Unstable Manifolds
. 46
2.3
Phase Portraits of Linear Systems in the Plane
. 49
vi
Contents
2.4
Linearization and Hartman's Theorem
. 54
2.5
Constructing Phase Plane Diagrams
. 55
2.6
Mathematica
Commands in Text Format
. 64
2.7
Exercises
. 65
3
Interacting Species
69
3.1
Competing Species
. 69
3.2
Predator-Prey Models
. 72
3.3
Other Characteristics Affecting Interacting Species
. 78
3.4
Mathematica
Commands in Text Format
. 80
3.5
Exercises
. 81
4
Limit Cycles
85
4.1
Historical Background
. 86
4.2
Existence and Uniqueness of Limit Cycles in the Plane
. 89
4.3
Nonexistence of Limit Cycles in the Plane
. 95
4.4
Perturbation Methods
. 98
4.5
Mathematica
Commands in Text Format
. 106
4.6
Exercises
. 107
5
Hamiltonian Systems, Lyapunov Functions, and Stability 111
5.1
Hamiltonian Systems in the Plane
. 112
5.2
Lyapunov Functions and Stability
. 117
5.3
Mathematica
Commands in Text Format
. 122
5.4
Exercises
. 123
6
Bifurcation Theory
127
6.1
Bifurcations of Nonlinear Systems in the Plane
. 128
6.2
Normal Forms
. 134
6.3
Multistability and Bistability
. 137
6.4
Mathematica
Commands in Text Format
. 140
6.5
Exercises
. 140
7
Three-Dimensional Autonomous Systems and Chaos
145
7.1
Linear Systems and Canonical Forms
. 146
7.2
Nonlinear Systems and Stability
. 150
7.3
The
Rössler
System and Chaos
. 154
7.4
The
Lorenz
Equations, Chua's Circuit, and the
Belousov-Zhabotinski Reaction
. 158
7.5
Mathematica
Commands in Text Format
. 165
7.6
Exercises
. 166
8
Poincaré
Maps and Nonautonomous Systems in the Plane
171
8.1
Poincaré
Maps
. 172
Contents
vii
8.2 Hamiltonian Systems
with Two Degrees of Freedom
. 178
8.3
Nonautonomous Systems in the Plane
. 181
8.4
Mathematica
Commands in Text Format
. 189
8.5
Exercises
. 192
9
Local and Global Bifurcations
195
9.1
Small-Amplitude Limit Cycle Bifurcations
. 196
9.2 Gröbner
Bases
. 201
9.3
Melnikov Integrals and Bifurcating Limit Cycles from a
Center
. 207
9.4
Bifurcations Involving Homoclinic Loops
. 209
9.5
Mathematica
Commands in Text Format
. 211
9.6
Exercises
. 213
10
The Second Part of Hilbert's Sixteenth Problem
217
10.1
Statement of Problem and Main Results
. 218
10.2
Poincaré Compactification
. 220
10.3
Global Results for
Liénard
Systems
. 227
10.4
Local Results for
Liénard
Systems
. 235
10.5
Exercises
. 237
11
Linear Discrete Dynamical Systems
241
11.1
Recurrence Relations
. 242
11.2
The Leslie Model
. 247
11.3
Harvesting and Culling Policies
. 251
11.4
Mathematica
Commands in Text Format
. 255
11.5
Exercises
. 256
12
Nonlinear Discrete Dynamical Systems
261
12.1
The Tent Map and Graphical Iterations
. 262
12.2
Fixed Points and Periodic Orbits
. 266
12.3
The Logistic Map, Bifurcation Diagram, and
Feigenbaum
Number
. 273
12.4
Gaussian and
Hénon
Maps
. 281
12.5
Applications
. 285
12.6
Mathematica
Commands in Text Format
. 288
12.7
Exercises
. 289
13
Complex Iterative Maps
293
13.1
Julia Sets and the Mandelbrot Set
. 294
13.2
Boundaries of Periodic Orbits
. 298
13.3
Mathematica
Commands in Text Format
. 300
13.4
Exercises
. 302
viii Contents
14
Electromagnetic
Waves and Optical Resonators
305
14.1
Maxwell's Equations and Electromagnetic Waves
.306
14.2
Historical Background
.308
14.3
The Nonlinear
SFR
Resonator
.312
14.4
Chaotic Attractors and Bistability
.314
14.5
Linear Stability Analysis
.318
14.6
Instabilities and Bistability
.321
14.7
Mathematica
Commands in Text Format
.325
14.8
Exercises
.327
15
Fractals and
Multirraciais
331
15.1
Construction of Simple Examples
.332
15.2
Calculating Fractal Dimensions
.338
15.3
A Multifractal Formalism
.343
15.4
Multirraciais
in the Real World and Some Simple Examples
. . . 348
15.5
Mathematica
Commands in Text Format
.356
15.6
Exercises
.357
16
Chaos Control and Synchronization
363
16.1
Historical Background
.364
16.2
Controlling Chaos in the Logistic Map
.368
16.3
Controlling Chaos in the
Hénon
Map
.372
16.4
Chaos Synchronization
.376
16.5
Mathematica
Commands in Text Format
.379
16.6
Exercises
.381
17
Neural Networks
387
17.1
Introduction
.388
17.2
The Delta Learning Rule and Backpropagation
.394
17.3
The Hopfield Network and Lyapunov Stability
.398
17.4
Neurodynamics
.408
17.5
Mathematica
Commands in Text Format
.411
17.6
Exercises
.415
18
Examination-Type Questions
421
18.1
Dynamical Systems with Applications
.421
18.2
Dynamical Systems with
Mathematica
.424
19
Solutions to Exercises
429
19.0
Chapter
0 .429
19.1
Chapter
1 .431
19.2
Chapter
2 .431
19.3
Chapters
.433
19.4
Chapter
4 .435
Contents ix
19.5
Chapter
5 . 436
19.6
Chapter
6 . 437
19.7
Chapter?
. 438
19.8
Chapter
8 . 439
19.9
Chapter
9 . 440
19.10
Chapter
10. 440
19.11
Chapter
11. 442
19.12
Chapter
12. 444
19.13
Chapter
13. 445
19.14
Chapter
14. 446
19.15
Chapter
15. 446
19.16
Chapter
16. 447
19.17
Chapter
17. 447
19.18
Chapter
18. 448
References
451
Textbooks
.451
Research Papers
.459
Mathematica
Program Index
469
Index
473 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Lynch, Stephen 1964- |
| author_GND | (DE-588)122765052 |
| author_facet | Lynch, Stephen 1964- |
| author_role | aut |
| author_sort | Lynch, Stephen 1964- |
| author_variant | s l sl |
| building | Verbundindex |
| bvnumber | BV023069248 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.8 |
| callnumber-search | QA614.8 |
| callnumber-sort | QA 3614.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 5200 SK 810 ST 601 |
| classification_tum | MAT 344f MAT 306f |
| ctrlnum | (OCoLC)209981286 (DE-599)BVBBV023069248 |
| dewey-full | 515.3922 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 22 |
| dewey-search | 515.39 22 |
| dewey-sort | 3515.39 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik Philosophie |
| discipline_str_mv | Informatik Mathematik Philosophie |
| format | Book |
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| id | DE-604.BV023069248 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:32:19Z |
| indexdate | 2024-07-09T21:10:17Z |
| institution | BVB |
| isbn | 9780817644826 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016272410 |
| oclc_num | 209981286 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-29T DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-M347 DE-898 DE-BY-UBR DE-473 DE-BY-UBG DE-11 DE-188 |
| owner_facet | DE-19 DE-BY-UBM DE-29T DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-M347 DE-898 DE-BY-UBR DE-473 DE-BY-UBG DE-11 DE-188 |
| physical | XV, 484 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Lynch, Stephen 1964- Verfasser (DE-588)122765052 aut Dynamical systems with applications using Mathematica Stephen Lynch Boston, Mass. [u.a.] Birkhäuser 2007 XV, 484 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [451] - 468 "The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering, Many chapters of the book are especially useful as reference material for senior undergraduate independent project work."--BOOK JACKET. Mathematica (Computer file) Datenverarbeitung Differential dynamical systems Data processing Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Mathematica 11.3 (DE-588)1173190325 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Mathematica Programm (DE-588)4268208-3 s 1\p DE-604 Mathematica 11.3 (DE-588)1173190325 s 2\p DE-604 Erscheint auch als Online-Ausgabe 978-0-8176-4586-1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016272410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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 | Lynch, Stephen 1964- Dynamical systems with applications using Mathematica Mathematica (Computer file) Datenverarbeitung Differential dynamical systems Data processing Mathematica Programm (DE-588)4268208-3 gnd Mathematica 11.3 (DE-588)1173190325 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4268208-3 (DE-588)1173190325 (DE-588)4013396-5 |
| title | Dynamical systems with applications using Mathematica |
| title_auth | Dynamical systems with applications using Mathematica |
| title_exact_search | Dynamical systems with applications using Mathematica |
| title_exact_search_txtP | Dynamical systems with applications using Mathematica |
| title_full | Dynamical systems with applications using Mathematica Stephen Lynch |
| title_fullStr | Dynamical systems with applications using Mathematica Stephen Lynch |
| title_full_unstemmed | Dynamical systems with applications using Mathematica Stephen Lynch |
| title_short | Dynamical systems with applications using Mathematica |
| title_sort | dynamical systems with applications using mathematica |
| topic | Mathematica (Computer file) Datenverarbeitung Differential dynamical systems Data processing Mathematica Programm (DE-588)4268208-3 gnd Mathematica 11.3 (DE-588)1173190325 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Mathematica (Computer file) Datenverarbeitung Differential dynamical systems Data processing Mathematica Programm Mathematica 11.3 Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016272410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lynchstephen dynamicalsystemswithapplicationsusingmathematica |