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Applied nonlinear dynamics: analytical, computational, and experimental methods

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Bibliographische Detailangaben
Beteiligte Personen:	Nayfeh, Ali Hasan 1933-2017 (VerfasserIn), Balachandran, Balakumar (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York u.a. Wiley 1995
Schriftenreihe:	Wiley series in nonlinear science
Schlagwörter:	Nichtlineare Dynamik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006851003&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XV, 685 S. graph. Darst.
ISBN:	0471593486

Internformat

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Datensatz im Suchindex

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adam_text	CONTENTS PREFACE xiii 1 INTRODUCTION 1 1.1 DISCRETE TIME 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 Poincare 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 POINCARE 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 QUASIPERIODIC SOLUTIONS 231 4.1 POINCARE MAPS 233 4.1.1 Winding Time and Rotation Number 238 4.1.2 Second Order Poincare Map 240 4.1.3 Comments 241 4.2 CIRCLE MAP 242 4.3 CONSTRUCTIONS 248 4.3.1 Method of Multiple Scales 249 4.3.2 Spectral Balance Method 251 4.3.3 Poincare Map Method 253 4.4 STABILITY 254 4.5 SYNCHRONIZATION 255 4.6 EXERCISES 269 5 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 x 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 Poincare 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 POINCARE SECTIONS AND MAPS 514 CONTENTS xi 7.6.1 Systems of Equations 514 7.6.2 Experiments 516 7.6.3 Higher Order Poincare 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
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physical	XV, 685 S. graph. Darst.
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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_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=006851003&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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