Verfügbarkeit: Hyperbolic chaos | Technische Universität München

Hyperbolic chaos: a physicist's view

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Bibliographische Detailangaben
Beteilige Person:	Kuznecov, Sergej P. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Beijing Higher Education Press 2012 Berlin Springer
Schlagwörter:	Nichtlineare Dynamik Hyperbolizität Attraktor Chaotisches System
Links:	http://deposit.dnb.de/cgi-bin/dokserv?id=3863665&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024780899&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Literaturangaben
Umfang:	XV, 320 S. Ill., graph. Darst.
ISBN:	9783642236662 9787040319644 9783642236655 3642236650

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Datensatz im Suchindex

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adam_text	IMAGE 1 CONTENTS PART I BASIC NOTIONS AND REVIEW 1 DYNAMICAL SYSTEMS AND HYPERBOLICITY 3 1.1 DYNAMICAL SYSTEMS: BASIC NOTIONS 3 1.1.1 SYSTEMS WITH CONTINUOUS AND DISCRETE TIME, AND THEIR MUTUAL RELATION 3 1.1.2 DYNAMICS IN TERMS OF PHASE FLUID: CONSERVATIVE AND DISSIPATIVE SYSTEMS AND ATTRACTORS 6 1.1.3 ROUGH SYSTEMS AND STRUCTURAL STABILITY 8 1.1.4 LYAPUNOV EXPONENTS AND THEIR COMPUTATION 10 1.2 MODEL EXAMPLES OF CHAOTIC ATTRACTORS 12 1.2.1 CHAOS IN TERMS OF PHASE FLUID AND BAKER S MAP 12 1.2.2 SMALE-WILLIAMS SOLENOID 15 1.2.3 DA-ATTRACTOR 16 1.2.4 PLYKIN TYPE ATTRACTORS 17 1.3 NOTION OF HYPERBOLICITY 19 1.4 CONTENT AND CONCLUSIONS OF THE HYPERBOLIC THEORY 22 1.4.1 CONE CRITERION 24 1.4.2 INSTABILITY 25 1.4.3 TRANSVERSAL CANTOR STRUCTURE AND KAPLAN-YORKE DIMENSION 25 1.4.4 MARKOV PARTITION AND SYMBOLIC DYNAMICS 26 1.4.5 ENUMERATING OF ORBITS AND TOPOLOGICAL ENTROPY 27 1.4.6 STRUCTURAL STABILITY 28 1.4.7 INVARIANT MEASURE OF SINAI-RUELLE-BOWEN 29 1.4.8 SHADOWING AND EFFECT OF NOISE 30 1.4.9 ERGODICITY AND MIXING 30 1.4.10 KOLMOGOROV-SINAI ENTROPY 31 REFERENCES 31 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1014072662 DIGITALISIERT DURCH IMAGE 2 JYJ CONTENTS 2 POSSIBLE OCCURRENCE OF HYPERBOLIC ATTRACTORS 35 2.1 THE NEWHOUSE-RUELLE-TAKENS THEOREM AND ITS RELATION TO THE UNIFORMLY HYPERBOLIC ATTRACTORS 35 2.2 LORENZ MODEL AND ITS MODIFICATIONS 37 2.3 SOME MAPS WITH UNIFORMLY HYPERBOLIC ATTRACTORS 40 2.4 FROM DA TO THE PLYKIN TYPE ATTRACTOR 43 2.5 HUNT S EXAMPLE: SUSPENDING THE PLYKIN TYPE ATTRACTOR 46 2.6 THE TRIPLE LINKAGE: A MECHANICAL SYSTEM WITH HYPERBOLIC DYNAMICS 49 2.7 A POSSIBLE OCCURRENCE OF A PLYKIN TYPE ATTRACTOR IN HINDMARSH-ROSE NEURON MODEL 51 2.8 BLUE SKY CATASTROPHE AND BIRTH OF THE SMALE-WILLIAMS ATTRACTOR 52 2.9 TAFFY-PULLING MACHINE 53 REFERENCES 54 PART II LOW-DIMENSIONAL MODELS 3 KICKED MECHANICAL MODELS AND DIFFERENTIAL EQUATIONS WITH PERIODIC SWITCH 59 3.1 SMALE-WILLIAMS SOLENOID IN MECHANICAL MODEL: MOTION OF A PARTICLE ON A PLANE UNDER PERIODIC KICKS 60 3.2 A SET OF SWITCHING DIFFERENTIAL EQUATIONS WITH ATTRACTOR OF SMALE-WILLIAMS TYPE 65 3.3 EXPLICIT DYNAMICAL SYSTEM WITH ATTRACTOR OF PLYKIN TYPE 68 3.3.1 PLYKIN TYPE ATTRACTOR ON A SPHERE 68 3.3.2 PLYKIN TYPE ATTRACTOR ON THE PLANE 73 3.4 PLYKIN-LIKE ATTRACTOR IN SMOOTH NON-AUTONOMOUS SYSTEM 76 REFERENCES 79 4 NON-AUTONOMOUS SYSTEMS OF COUPLED SELF-OSCILLATORS 81 4.1 VAN DER POL OSCILLATOR 81 4.2 SMALE-WILLIAMS ATTRACTOR IN A NON-AUTONOMOUS SYSTEM OF ALTERNATELY EXCITED VAN DER POL OSCILLATORS 84 4.3 SYSTEM OF ALTERNATELY EXCITED VAN DER POL OSCILLATORS IN TERMS OF SLOW COMPLEX AMPLITUDES 93 4.4 NON-RESONANCE EXCITATION TRANSFER 94 4.5 PLYKIN-LIKE ATTRACTOR IN NON-AUTONOMOUS COUPLED OSCILLATORS 95 4.5.1 REPRESENTATION OF STATES ON A SPHERE AND EQUATIONS OF THE MODEL 95 4.5.2 NUMERICAL RESULTS FOR THE COUPLED OSCILLATORS 98 REFERENCES 101 5 AUTONOMOUS LOW-DIMENSIONAL SYSTEMS WITH UNIFORMLY HYPERBOLIC ATTRACTORS IN THE POINCARE MAPS 103 5.1 AUTONOMOUS SYSTEM OF TWO COUPLED OSCILLATORS WITH SELF-REGULATING ALTERNATING EXCITATION 103 IMAGE 3 CONTENTS XIII 5.2 SYSTEM CONSTRUCTED ON A BASE OF THE PREDATOR-PREY MODEL 107 5.3 EXAMPLE OF BLUE SKY CATASTROPHE ACCOMPANIED BY A BIRTH OF SMALE-WILLIAMS ATTRACTOR 112 REFERENCES 117 6 PARAMETRIC GENERATORS OF HYPERBOLIC CHAOS 119 6.1 PARAMETRIC EXCITATION OF COUPLED OSCILLATORS. THREE-FREQUENCY PARAMETRIC GENERATOR AND ITS OPERATION 120 6.2 HYPERBOLIC CHAOS IN PARAMETRIC OSCILLATOR WITH Q-SWITCH AND PUMP MODULATION 123 6.2.1 DYNAMICAL EQUATIONS 123 6.2.2 QUALITATIVE EXPLANATION OF THE OPERATION 126 6.2.3 NUMERICAL RESULTS 127 6.2.4 NUMERICAL RESULTS IN THE FRAME OF METHOD OF SLOW COMPLEX AMPLITUDES 129 6.3 PARAMETRIC GENERATOR OF HYPERBOLIC CHAOS BASED ON FOUR COUPLED OSCILLATORS WITH PUMP MODULATION 131 6.3.1 MODEL, OPERATION PRINCIPLE AND BASIC EQUATIONS 132 6.3.2 CHAOTIC DYNAMICS: RESULTS OF COMPUTER SIMULATION 134 REFERENCES 139 7 RECOGNIZING THE HYPERBOLIDTY: CONE CRITERION AND OTHER APPROACHES 141 7.1 VERIFICATION OF TRANSVERSALITY FOR MANIFOLDS 141 7.1.1 VISUALIZATION OF THE MANIFOLDS 142 7.1.2 DISTRIBUTIONS OF ANGLES OF THE MANIFOLD INTERSECTIONS 144 7.2 VISUALIZATION OF INVARIANT MEASURES 150 7.3 CONE CRITERION AND EXAMPLES OF ITS APPLICATION 155 7.3.1 PROCEDURE OF VERIFICATION OF THE CONE CRITERION 155 7.3.2 EXAMPLES OF APPLICATION OF THE CONE CRITERION 161 REFERENCES 169 PART III HIGHER-DIMENSIONAL SYSTEMS AND PHENOMENA 8 SYSTEMS OF FOUR ALTERNATELY EXCITED NON-AUTONOMOUS OSCILLATORS . .. 173 8.1 ARNOLD S CAT MAP DYNAMICS IN A SYSTEM OF COUPLED NON-AUTONOMOUS VAN DER POL OSCILLATORS 173 8.2 DYNAMICS CORRESPONDING TO HYPERCHAOTIC MAPS 180 8.2.1 SYSTEM IMPLEMENTING TORAL HYPERCHAOTIC MAP 180 8.2.2 MODEL WITH CASCADE TRANSFER OF EXCITATION UPWARD THE FREQUENCY SPECTRUM 182 8.3 HYPERCHAOS AND SYNCHRONOUS CHAOS IN A SYSTEM OF COUPLED NON-AUTONOMOUS OSCILLATORS 187 8.3.1 EQUATIONS AND BASIC MODES OF OPERATION 188 8.3.2 EQUATIONS FOR SLOW COMPLEX AMPLITUDES 193 REFERENCES 199 IMAGE 4 JYY CONTENTS 9 AUTONOMOUS SYSTEMS BASED ON DYNAMICS CLOSE TO HETERODINIC CYCLE 201 9.1 HETEROCLINIC CONNECTION: AN EXAMPLE OF GUCKENHEIMER AND HOLMES 201 9.2 ATTRACTOR OF SMALE-WILLIAMS TYPE IN A SYSTEM OF THREE COUPLED SELF-OSCILLATORS 203 9.3 ATTRACTOR WITH DYNAMICS GOVERNED BY THE ARNOLD CAT MAP 207 9.4 MODEL WITH HYPERCHAOS 210 9.5 AN AUTONOMOUS SYSTEM WITH ATTRACTOR OF SMALE-WILLIAMS TYPE WITH RESONANCE TRANSFER OF EXCITATION IN A RING ARRAY OF VAN DER POL OSCILLATORS 213 REFERENCES 217 10 SYSTEMS WITH TIME-DELAY FEEDBACK 219 10.1 SOME NOTIONS CONCERNING DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT 220 10.2 VAN DER POL OSCILLATOR WITH DELAYED FEEDBACK, PARAMETER MODULATION AND AUXILIARY SIGNAL 223 10.2.1 ATTRACTOR OF SMALE-WILLIAMS TYPE IN THE TIME-DELAYED SYSTEM 224 10.2.2 HYPERCHAOTIC ATTRACTORS 227 10.3 VAN DER POL OSCILLATOR WITH TWO DELAYED FEEDBACK LOOPS AND PARAMETER MODULATION 231 10.4 AUTONOMOUS TIME-DELAY SYSTEM 237 REFERENCES 240 11 CHAOS IN CO-OPERATIVE DYNAMICS OF ALTERNATELY SYNCHRONIZED ENSEMBLES OF GLOBALLY COUPLED SELF-OSCILLATORS 243 11.1 KURAMOTO TRANSITION IN ENSEMBLE OF GLOBALLY COUPLED OSCILLATORS . .. 243 11.2 MODEL OF TWO ALTERNATELY SYNCHRONIZED ENSEMBLES OF OSCILLATORS . . .. 247 11.2.1 COLLECTIVE CHAOS IN ENSEMBLE OF VAN DER POL OSCILLATORS 248 11.2.2 SLOW-AMPLITUDE APPROACH 251 11.2.3 DESCRIPTION OF THE DYNAMICS IN TERMS OF ENSEMBLES OF PHASE OSCILLATORS 254 REFERENCES 256 PARTRV EXPERIMENTAL STUDIES 12 ELECTRONIC DEVICE WITH ATTRACTOR OF SMALE-WILLIAMS TYPE 259 12.1 SCHEME OF THE DEVICE AND THE PRINCIPLE OF OPERATION 259 12.2 EXPERIMENTAL OBSERVATION OF THE SMALE-WILLIAMS ATTRACTOR 260 REFERENCES 263 IMAGE 5 CONTENTS XV 13 DELAY-TIME ELECTRONIC DEVICES GENERATING TRAINS OF OSCILLATIONS WITH PHASES GOVERNED BY CHAOTIC MAPS 265 13.1 VAN DER POL OSCILLATOR WITH DELAYED FEEDBACK, PARAMETER MODULATION AND AUXILIARY SIGNAL 265 13.2 VAN DER POL OSCILLATOR WITH TWO DELAYED FEEDBACK LOOPS AND PARAMETER MODULATION 269 REFERENCES 272 14 CONCLUSION 273 REFERENCES 275 APPENDIX A COMPUTATION OF LYAPUNOV EXPONENTS: THE BENETTIN ALGORITHM 277 REFERENCES 279 APPENDIX B HENON AND IKEDA MAPS 281 REFERENCES 287 APPENDIX C SMALE S HORSESHOE AND HOMOCLINIC TANGLE 289 REFERENCES 292 APPENDIX D FRACTAL DIMENSIONS AND KAPLAN-YORKE FORMULA 293 REFERENCES 297 APPENDIX E HUNT S MODEL: FORMAL DEFINITION 299 REFERENCES 303 APPENDIX F GEODESIES ON A COMPACT SURFACE OF NEGATIVE CURVATURE 305 REFERENCES 309 APPENDIX G EFFECT OF NOISE IN A SYSTEM WITH A HYPERBOLIC ATTRACTOR 311 REFERENCES 317 INDEX 319
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spellingShingle	Kuznecov, Sergej P. Hyperbolic chaos a physicist's view Nichtlineare Dynamik (DE-588)4126141-0 gnd Hyperbolizität (DE-588)4710615-3 gnd Attraktor (DE-588)4140563-8 gnd Chaotisches System (DE-588)4316104-2 gnd
subject_GND	(DE-588)4126141-0 (DE-588)4710615-3 (DE-588)4140563-8 (DE-588)4316104-2
title	Hyperbolic chaos a physicist's view
title_auth	Hyperbolic chaos a physicist's view
title_exact_search	Hyperbolic chaos a physicist's view
title_full	Hyperbolic chaos a physicist's view Sergey P. Kuznetsov
title_fullStr	Hyperbolic chaos a physicist's view Sergey P. Kuznetsov
title_full_unstemmed	Hyperbolic chaos a physicist's view Sergey P. Kuznetsov
title_short	Hyperbolic chaos
title_sort	hyperbolic chaos a physicist s view
title_sub	a physicist's view
topic	Nichtlineare Dynamik (DE-588)4126141-0 gnd Hyperbolizität (DE-588)4710615-3 gnd Attraktor (DE-588)4140563-8 gnd Chaotisches System (DE-588)4316104-2 gnd
topic_facet	Nichtlineare Dynamik Hyperbolizität Attraktor Chaotisches System
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