Introduction to discrete dynamical systems and chaos
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| Format: | Buch |
| Sprache: | English |
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New York [u.a.]
Wiley
1999
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| Schriftenreihe: | A Wiley interscience publication
Wiley interscience series in discrete mathematics and optimization |
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| 245 | 1 | 0 | |a Introduction to discrete dynamical systems and chaos |c Mario Martelli |
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| adam_text | IMAGE 1
INTRODUCTION TO DISCRETE DYNAMICAL
SYSTEMS AND CHAOS
MARIO MARTELLI CALIFORNIA STATE UNIVERSITY FULLERTON
A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. NEW YORK *
CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO
IMAGE 2
CONTENTS
CHAPTER 1. DISCRETE DYNAMICAL SYSTEMS 1
SECTION 1. DISCRETE DYNAMICAL SYSTEMS: DEFINITION 2
1. EXAMPLES OF DISCRETE DYNAMICAL SYSTEMS 2
2. DEFINITION OF DISCRETE DYNAMICAL SYSTEMS 9
GOALS OFTHIS BOOK 12
SECTION 2. STATIONARY STATES AND PERIODIC ORBITS 16
1. STATIONARY STATES 16
STABLE STATIONARY STATES 18
2. PERIODIC ORBITS 21
STABLE PERIODIC ORBITS 23
SECTION 3. CHAOTIC DYNAMICAL SYSTEMS 25
1. LIMIT POINTS, LIMIT SETS, AND APERIODIC ORBITS 25
2. UNSTABLE ORBITS AND CHAOTIC SYSTEMS 30
CHAOTIC BEHAVIOR 33
SECTION 4. EXAMPLES OF DISCRETE DYNAMICAL SYSTEMS 34
ONE-DIMENSIONAL EXAMPLE: BLOOD-CELL BIOLOGY 34
TWO-DIMENSIONAL EXAMPLES: PREDATOR-PREY MODELS 36
THREE-DIMENSIONAL EXAMPLE: METEOROLOGY 40
MULTIDIMENSIONAL EXAMPLE: NEURAL NETWORKS 42
CHAPTER 2. ONE-DIMENSIONAL DYNAMICAL SYSTEMS 45
SECTION 1. COBWEB AND CONJUGACY 46
1. THE COBWEB METHOD 46
2. CONJUGACY 50
LINEAR AND AFFINE SYSTEMS 53
SECTION 2. SINKS AND SOURCES 55
1. STATIONARY STATES AND PERIODIC ORBITS 55
2. SINKS 60
3. SOURCES 66
INSTABILITY 69
SECTION 3. GLOBAL SINKS 71
SECTION 4. PARAMETER SPACE ANALYSIS 75
1. FOLD, TRANSCRITICAL, AND PITCHFORK BIFURCATION 75
2. PERIOD-DOUBLING BIFURCATION 81
3. BIFURCATION: A THEORETICAL VIEWPOINT 85
SECTION 5. CONJUGACY AND CHAOS 93
ORBITS OF CONJUGATE SYSTEMS 93
CHAOS IN THELI-YORKE SENSE 95
CHAPTER 3. R1, MATRICES, AND FUNCTIONS 99
SECTION 1. STRUCTURE OF R1 AND CONTINUITY 100
V II
IMAGE 3
V I II CONTENTS
1. NORMSAND SETS 100
VECTORS AND POINTS 100
EUCLIDEAN NORM 102
SUBSETS OF R1 102
OTHERNORMS 104
2. CONTINUITY 106
SECTION 2. OPERATOR NORM AND DERIVATIVE 111
1. OPERATOR NORM 111
OPERATOR NORM OF A MATRIX 113
2. DERIVATIVE AND MEAN VALUE INEQUALITY 117
FIRST-ORDER APPROXIMATION 118
MEAN VALUE INEQUALITY 120
CHAPTER 4. DISCRETE LINEAR DYNAMICAL SYSTEMS 123
SECTION 1. ORBITS OF LINEAR PROCESSES 124
SECTION 2. STABILITY AND INSTABILITY OF THE ORIGIN 127
THE ORIGIN AS AN ATTRACTOR 127
THE ORIGIN AS AREPELLER 128
SECTION 3. SPECTRAL DECOMPOSITION THEOREM 131
SDT: REAL, SEMISIMPLE EIGENVALUES 134
SDT: REAL, NOT SEMISIMPLE EIGENVALUES (*) 137
SDT: WHEN A(M) HAS COMPLEX ELEMENTS (*) 139
SECTION 4. THE ORIGIN AS A SADDLE POINT 146
STABLE AND UNSTABLE SUBSPACES 146
COMPARING TRAJECTORIES 149
SECTION 5. EIGENVALUES WITH MODULUS 1 (*) 151
THE ACTION OF M ON X { 152
THE ACTION OF M ON X_] 154
THE ACTION OF M ON X C 156
SECTION 6. AFFINE SYSTEMS 161
WHEN 1 IS NOT AN EIGENVALUE 161
WHEN 1 IS AN EIGENVALUE (*) 163
CHAPTER 5. NONLINEAR DYNAMICAL SYSTEMS 169
SECTION 1. BOUNDED INVARIANT SETS 170
CONTRACTIONS 170
DISSIPATIVE MAPS 171
QUASI-BOUNDED MAPS 173
SECTION 2. GLOBAL STABILITY OF FIXED POINTS 176
BANACH CONTRACTION PRINCIPLE 176
TRIANGULAER MAPS 177
GRADIENT MAPS (*) 179
SECTION 3. SINKS 182
SECTION 4. REPELLERS AND SADDLES 187
REPELLING STATES 187
SADDLES 189
SECTION 5. BIFURCATION 192
BIFURCATION FROM THE TRIVIAL BRANCH: X(A)=0 193
IMAGE 4
CONTENTS IX
HOPF BIFURCATION 196
CHAPTER 6. CHAOTIC BEHAVIOR 199
SECTION 1. ATTRACTORS 200
SECTION 2. CHAOTIC DYNAMICAL SYSTEMS 205
LI-YORKE CHAOS IN R1 211
SECTION 3. FRACTAL DIMENSION 216
CAPACITY 217
CORRELATION DIMENSION 220
SECTION 4. LYAPUNOV EXPONENTS 227
CHAPTER 7. ANALYSIS OF FOUR DYNAMICAL SYSTEMS 237
SECTION 1. BLOOD-CELL POPULATION MODEL 238
SECTION 2. PREDATOR-PREY MODELS 243
SECTION 3. LORENZ MODEL OF ATMOSPHERIC BEHAVIOR 250
SECTION 4. NEURAL NETWORKS 256
APPENDIX 1. MATHEMATICA PROGRAMS 263
SECTION 1. GRAPHING 264
1. GRAPHING FUNCTIONS 264
2. FINDING FIXED POINTS AND PERIODIC ORBITS GRAPHICALLY 269 3. THE
COBWEB METHOD 271
SECTION 2. ITERATES AND ORBITS 273
1. ITERATES 273
2. ORBITS 275
3. ORBITS OF TWO-DIMENSIONAL SYSTEMS 283
4. ORBITS OF LINEAR SYSTEMS 285
SECTION 3. BIFURCATION DIAGRAMS, LYAPUNOV EXPONENTS, AND CORRELATION
DIMENSION 286
1. BIFURCATION DIAGRAMS 286
2. LYAPUNOV EXPONENTS 290
3. CORRELATION DIMENSION 293
SECTION 4. ODDS AND ENDS 296
1. MATRICES AND VECTORS OPERATIONS 296
2. SOLVING EQUATIONS 297
3. ASSIGNING A NUMERICAL VALUE TO THE RESULT OF AN OPERATION 299
APPENDIX 2. REFERENCES AND PROJECTS 301
1. REFERENCES 301
2. PROJECTS 305
APPENDIX 3. ANSWERS TO SELECTED PROBLEMS 311
INDEX 327
|
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| author | Martelli, Mario 1937- |
| author_GND | (DE-588)138611092 |
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| ctrlnum | (OCoLC)246608197 (DE-599)BVBBV012660942 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:31:27Z |
| institution | BVB |
| isbn | 0471319759 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008602742 |
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| owner_facet | DE-703 DE-11 |
| physical | XIII, 328 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley interscience publication Wiley interscience series in discrete mathematics and optimization |
| spelling | Martelli, Mario 1937- Verfasser (DE-588)138611092 aut Introduction to discrete dynamical systems and chaos Mario Martelli New York [u.a.] Wiley 1999 XIII, 328 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley interscience publication Wiley interscience series in discrete mathematics and optimization Dynamisches System (DE-588)4013396-5 gnd rswk-swf Diskretes System (DE-588)4401225-1 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Diskretes System (DE-588)4401225-1 s Dynamisches System (DE-588)4013396-5 s Chaotisches System (DE-588)4316104-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008602742&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martelli, Mario 1937- Introduction to discrete dynamical systems and chaos Dynamisches System (DE-588)4013396-5 gnd Diskretes System (DE-588)4401225-1 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4401225-1 (DE-588)4316104-2 |
| title | Introduction to discrete dynamical systems and chaos |
| title_auth | Introduction to discrete dynamical systems and chaos |
| title_exact_search | Introduction to discrete dynamical systems and chaos |
| title_full | Introduction to discrete dynamical systems and chaos Mario Martelli |
| title_fullStr | Introduction to discrete dynamical systems and chaos Mario Martelli |
| title_full_unstemmed | Introduction to discrete dynamical systems and chaos Mario Martelli |
| title_short | Introduction to discrete dynamical systems and chaos |
| title_sort | introduction to discrete dynamical systems and chaos |
| topic | Dynamisches System (DE-588)4013396-5 gnd Diskretes System (DE-588)4401225-1 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Dynamisches System Diskretes System Chaotisches System |
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