Synergetic phenomena in active lattices: patterns, waves, solitons, chaos
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Springer series in synergetics
Physics and astronomy online library |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erscheint: Februar 2002 |
| Physical Description: | XVII, 357 S. Ill., graph. Darst. |
| ISBN: | 3540427155 |
Staff View
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Record in the Search Index
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| adam_text | VLADIMIR I. NEKORKIN MANUEL G. VELARDE SYNERGETIC PHENOMENA IN ACTIVE
LATTICES PATTERNS, WAVES, SOLITONS, CHAOS WITH 207 FIGURES ** SPRINGER
CONTENTS 1. INTRODUCTION: SYNERGETICS AND MODELS OF CONTINUOUS AND
DISCRETE ACTIVE MEDIA. STEADY STATES AND BASIC MOTIONS (WAVES,
DISSIPATIVE SOLITONS, ETC.) 1 1.1 BASIC CONCEPTS, PHENOMENA AND CONTEXT
1 1.2 CONTINUOUS MODELS 8 1.3 CHAIN AND LATTICE MODELS WITH CONTINUOUS
TIME 12 1.4 CHAIN AND LATTICE MODELS WITH DISCRETE TIME 15 2. SOLITARY
WAVES, BOUND SOLITON STATES AND CHAOTIC SOLITON TRAINS IN A DISSIPATIVE
BOUSSINESQ*KORTEWEG*DE VRIES EQUATION . 19 2.1 INTRODUCTION AND
MOTIVATION 19 2.2 MODEL EQUATION 21 2.3 TRAVELING WAVES 23 2.3.1 STEADY
STATES 24 2.3.2 LYAPUNOV FUNCTIONS 25 2.4 HOMOCLINIC ORBITS. PHASE-SPACE
ANALYSIS 26 2.4.1 INVARIANT SUBSPACES 26 2.4.2 AUXILIARY SYSTEMS 27
2.4.3 CONSTRUCTION OF REGIONS CONFINING THE UNSTABLE AND STABLE
MANIFOLDS W U AND W S 28 2.5 MULTILOOP HOMOCLINIC ORBITS AND
SOLITON-BOUND STATES 31 2.5.1 EXISTENCE OF MULTILOOP HOMOCLINIC ORBITS
31 2.5.2 SOLITONIC WAVES, SOLITON-BOUND STATES AND CHAOTIC
SOLITON-TRAINS 34 2.5.3 HOMOCLINIC ORBITS AND SOLITON-TRAINS. SOME
NUMERICAL RESULTS 35 2.6 FURTHER NUMERICAL RESULTS AND COMPUTER
EXPERIMENTS 39 2.6.1 EVOLUTIONARY FEATURES 40 2.6.2 NUMERICAL COLLISION
EXPERIMENTS 43 2.7 SALIENT FEATURES OF DISSIPATIVE SOLITONS 48 XIV
CONTENTS 3. SELF-ORGANIZATION IN A LONG JOSEPHSON JUNCTION 49 3.1
INTRODUCTION AND MOTIVATION 49 3.2 THE PERTURBED SINE-GORDON EQUATION 50
3.3 BIFURCATION DIAGRAM OF HOMOCLINIC TRAJECTORIES 51 3.4
CURRENT-VOLTAGE CHARACTERISTICS OF LONG JOSEPHSON JUNCTIONS 54 3.5
BIFURCATION DIAGRAM IN THE NEIGHBORHOOD OF * = 1 56 3.5.1 SPIRAL-LIKE
BIFURCATION STRUCTURES 56 3.5.2 HETEROCLINIC CONTOURS 58 3.5.3 THE
NEIGHBORHOOD OF * * 61 3.5.4 THE SETS {7*} AND {7*} 65 3.6 EXISTENCE OF
HOMOCLINIC ORBITS 67 3.6.1 LYAPUNOV FUNCTION 68 3.6.2 THE VECTOR FIELD
OF (3.4) ON TWO AUXILIARY SURFACES . . 69 3.6.3 AUXILIARY SYSTEMS 69
3.6.4 TUNNELS FOR MANIFOLDS OF THE SADDLE STEADY STATE 0 2 70 3.6.5
HOMOCLINIC ORBITS 71 3.7 SALIENT FEATURES OF THE PERTURBED SINE-GORDON
EQUATION 74 4. SPATIAL STRUCTURES, WAVE FRONTS, PERIODIC WAVES, PULSES
AND SOLITARY WAVES IN A ONE-DIMENSIONAL ARRAY OF CHUA S CIRCUITS 77 4.1
INTRODUCTION AND MOTIVATION 77 4.2 SPATIO-TEMPORAL DYNAMICS OF AN ARRAY
OF RESISTIVELY COUPLED UNITS 79 4.2.1 STEADY STATES AND SPATIAL
STRUCTURES 80 4.2.2 WAVE FRONTS IN A GRADIENT APPROXIMATION 86 4.2.3
PULSES, FRONTS AND CHAOTIC WAVE TRAINS 94 4.3 SPATIO-TEMPORAL DYNAMICS
OF ARRAYS WITH INDUCTIVELY COUPLED UNITS 106 4.3.1 HOMOCLINIC ORBITS AND
SOLITARY WAVES 106 4.3.2 PERIODIC WAVES IN A CIRCULAR ARRAY 123 4.4
CHAOTIC ATTRACTORS AND WAVES IN A ONE-DIMENSIONAL ARRAY OF MODIFIED
CHUA S CIRCUITS 137 4.4.1 MODIFIED CHUA S CIRCUIT 137 4.4.2
ONE-DIMENSIONAL ARRAY 139 4.4.3 CHAOTIC ATTRACTORS 139 4.5 SALIENT
FEATURES OF CHUA S CIRCUIT IN A LATTICE 161 4.5.1 ARRAY WITH RESISTIVE
COUPLING 162 4.5.2 ARRAY WITH INDUCTIVE COUPLING 162 5. PATTERNS,
SPATIAL DISORDER AND WAVES IN A DYNAMICAL LATTICE OF BISTABLE UNITS 165
5.1 INTRODUCTION AND MOTIVATION 165 5.2 SPATIAL DISORDER IN A LINEAR
CHAIN OF COUPLED BISTABLE UNITS 166 CONTENTS XV 5.2.1 EVOLUTION OF
AMPLITUDES AND PHASES OF THE OSCILLATIONS 166 5.2.2 SPATIAL
DISTRIBUTIONS OF OSCILLATION AMPLITUDES 168 5.2.3 PHASE CLUSTERS IN A
CHAIN OF ISOCHRONOUS OSCILLATORS . . 171 5.3 CLUSTERING AND PHASE
RESETTING IN A CHAIN OF BISTABLE NONISOCHRONOUS OSCILLATORS 172 5.3.1
AMPLITUDE DISTRIBUTION ALONG THE CHAIN 173 5.3.2 PHASE CLUSTERS IN A
CHAIN OF NONISOCHRONOUS OSCILLATORS 175 5.3.3 FREQUENCY CLUSTERS AND
PHASE RESETTING 176 5.4 CLUSTERS IN AN ASSEMBLY OF GLOBALLY COUPLED
BISTABLE OSCILLATORS 179 5.4.1 HOMOGENEOUS OSCILLATIONS 180 5.4.2
AMPLITUDE CLUSTERS 181 5.4.3 AMPLITUDE-PHASE CLUSTERS 186 5.4.4
SPLAY-PHASE STATES 191 5.4.5 COLLECTIVE CHAOS 194 5.5 SPATIAL DISORDER
AND WAVES IN A CIRCULAR CHAIN OF BISTABLE UNITS 195 5.5.1 SPATIAL
DISORDER 195 5.5.2 SPACE-HOMOGENEOUS PHASE WAVES 197 5.5.3
SPACE-INHOMOGENEOUS PHASE WAVES 201 5.6 CHAOTIC AND REGULAR PATTERNS IN
TWO-DIMENSIONAL LATTICES OF COUPLED BISTABLE UNITS 206 5.6.1 METHODOLOGY
FOR A LATTICE OF BISTABLE ELEMENTS 206 5.6.2 STABLE STEADY STATES 209
5.6.3 SPATIAL DISORDER AND PATTERNS IN THE FITZHUGH-NAGUMO-SCHLOEGL MODEL
211 5.6.4 SPATIAL DISORDER AND PATTERNS IN A LATTICE OF BISTABLE
OSCILLATORS 212 5.7 PATTERNS AND SPIRAL WAVES IN A LATTICE OF EXCITABLE
UNITS . . . 216 5.7.1 PATTERN FORMATION 217 5.7.2 SPIRAL WAVE PATTERNS
219 5.8 SALIENT FEATURES OF NETWORKS OF BISTABLE UNITS 223 6. MUTUAL
SYNCHRONIZATION, CONTROL AND REPLICATION OF PATTERNS AND WAVES IN
COUPLED LATTICES COMPOSED OF BISTABLE UNITS 227 6.1 INTRODUCTION AND
MOTIVATION 227 6.2 LAYERED LATTICE SYSTEM AND MUTUAL SYNCHRONIZATION OF
TWO LATTICES 228 6.2.1 BISTABLE ELEMENTS OR UNITS 228 6.2.2 BISTABLE
OSCILLATORS 235 6.2.3 SYSTEM OF TWO COUPLED FIBERS 237 6.2.4 EXCITABLE
UNITS 250 XVI CONTENTS 6.3 CONTROLLED PATTERNS AND REPLICATION OF FORM
252 6.3.1 BISTABLE OSCILLATORS AND REPLICATION 252 6.3.2 EXCITABLE UNITS
270 6.4 SALIENT FEATURES OF REPLICATION PROCESSES VIA SYNCHRONIZATION OF
PATTERNS AND WAVES WITH INTERACTING BISTABLE UNITS 276 7.
SPATIO-TEMPORAL CHAOS IN BISTABLE COUPLED MAP LATTICES 279 7.1
INTRODUCTION AND MOTIVATION 279 7.2 SPECTRUM OF THE LINEARIZED OPERATOR
280 7.2.1 LINEAR OPERATOR 280 7.2.2 A FINITE-DIMENSIONAL APPROXIMATION
OF THE LINEAR OPERATOR 281 7.2.3 METHODOLOGY TO OBTAIN THE LINEAR
SPECTRUM 282 7.2.4 GERSHGORIN DISKS 283 7.2.5 AN ALTERNATIVE WAY TO
OBTAIN THE STABILITY CRITERION . 284 7.3 SPATIAL CHAOS IN A DISCRETE
VERSION OF THE ONE-DIMENSIONAL FITZHUGH-NAGUMO-SCHLOEGL EQUATION 284
7.3.1 SPATIAL CHAOS 284 7.3.2 A DISCRETE VERSION OF THE ONE-DIMENSIONAL
FITZHUGH-NAGUMO-SCHLOEGL EQUATION 285 7.3.3 STEADY STATES 285 7.3.4
STABILITY OF SPATIALLY STEADY SOLUTIONS 289 7.4 CHAOTIC TRAVELING WAVES
IN A ONE-DIMENSIONAL DISCRETE FITZHUGH-NAGUMO-SCHLOEGL EQUATION 292 7.4.1
TRAVELING WAVE EQUATION 292 7.4.2 EXISTENCE OF TRAVELING WAVES 293 7.4.3
STABILITY OF TRAVELING WAVES 295 7.5 TWO-DIMENSIONAL SPATIAL CHAOS 297
7.5.1 INVARIANT DOMAINS 297 7.5.2 EXISTENCE OF STEADY SOLUTIONS 300
7.5.3 STABILITY OF STEADY SOLUTIONS 300 7.5.4 TWO-DIMENSIONAL SPATIAL
CHAOS 301 7.6 SYNCHRONIZATION IN TWO-LAYER BISTABLE COUPLED MAP LATTICES
302 7.6.1 LAYERED COUPLED MAP LATTICES 302 7.6.2 DYNAMICS OF A SINGLE
LATTICE (LAYER) 307 7.6.3 GLOBAL INTERLAYER SYNCHRONIZATION 312 7.7
INSTABILITY OF THE SYNCHRONIZATION MANIFOLD 317 7.7.1 INSTABILITY OF THE
SYNCHRONIZED FIXED POINTS 317 7.7.2 INSTABILITY OF SYNCHRONIZED
ATTRACTORS AND ON-OFF INTERMITTENCY 319 7.8 SALIENT FEATURES OF COUPLED
MAP LATTICES 322 8. CONCLUSIONS AND PERSPECTIVE 325 CONTENTS XVII
APPENDICES 329 A. INTEGRAL MANIFOLDS OF STATIONARY POINTS 329 B.
RELATIVE LOCATION OF THE MANIFOLDS W*(0) AND W%(P+) 331 * FLOW
TRAJECTORIES ON THE MANIFOLDS W(0) AND W%(P + ) .... 332 D. INSTABILITY
OF SPATIALLY HOMOGENEOUS STATES 334 E. TOPOLOGICAL ENTROPY AND LYAPUNOV
EXPONENT 337 F. MULTIPLIERS OF THE FIXED POINT OF THE COUPLED MAP
LATTICE (7.55) 339 G. GERSHGORIN THEOREM 341 REFERENCES 343 SUBJECT
INDEX 355
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:57:09Z |
| institution | BVB |
| isbn | 3540427155 |
| language | English |
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| spelling | Nekorkin, Vladimir I. Verfasser (DE-588)1056126337 aut Synergetic phenomena in active lattices patterns, waves, solitons, chaos Vladimir I. Nekorkin ; Manuel G. Velarde Berlin [u.a.] Springer 2002 XVII, 357 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in synergetics Physics and astronomy online library Erscheint: Februar 2002 Chaos gtt Dynamique réticulaire Golven (algemeen, natuurkunde) gtt Niet-lineaire dynamica gtt Systèmes non linéaires Théories non linéaires Lattice dynamics Nonlinear systems Nonlinear theories Gittermodell (DE-588)4226961-1 gnd rswk-swf Mehrdimensionales System (DE-588)4431187-4 gnd rswk-swf Synergetik (DE-588)4058755-1 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Gittermodell (DE-588)4226961-1 s Nichtlineares dynamisches System (DE-588)4126142-2 s Mehrdimensionales System (DE-588)4431187-4 s Synergetik (DE-588)4058755-1 s DE-604 Velarde, Manuel G. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009638378&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nekorkin, Vladimir I. Velarde, Manuel G. Synergetic phenomena in active lattices patterns, waves, solitons, chaos Chaos gtt Dynamique réticulaire Golven (algemeen, natuurkunde) gtt Niet-lineaire dynamica gtt Systèmes non linéaires Théories non linéaires Lattice dynamics Nonlinear systems Nonlinear theories Gittermodell (DE-588)4226961-1 gnd Mehrdimensionales System (DE-588)4431187-4 gnd Synergetik (DE-588)4058755-1 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| subject_GND | (DE-588)4226961-1 (DE-588)4431187-4 (DE-588)4058755-1 (DE-588)4126142-2 |
| title | Synergetic phenomena in active lattices patterns, waves, solitons, chaos |
| title_auth | Synergetic phenomena in active lattices patterns, waves, solitons, chaos |
| title_exact_search | Synergetic phenomena in active lattices patterns, waves, solitons, chaos |
| title_full | Synergetic phenomena in active lattices patterns, waves, solitons, chaos Vladimir I. Nekorkin ; Manuel G. Velarde |
| title_fullStr | Synergetic phenomena in active lattices patterns, waves, solitons, chaos Vladimir I. Nekorkin ; Manuel G. Velarde |
| title_full_unstemmed | Synergetic phenomena in active lattices patterns, waves, solitons, chaos Vladimir I. Nekorkin ; Manuel G. Velarde |
| title_short | Synergetic phenomena in active lattices |
| title_sort | synergetic phenomena in active lattices patterns waves solitons chaos |
| title_sub | patterns, waves, solitons, chaos |
| topic | Chaos gtt Dynamique réticulaire Golven (algemeen, natuurkunde) gtt Niet-lineaire dynamica gtt Systèmes non linéaires Théories non linéaires Lattice dynamics Nonlinear systems Nonlinear theories Gittermodell (DE-588)4226961-1 gnd Mehrdimensionales System (DE-588)4431187-4 gnd Synergetik (DE-588)4058755-1 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| topic_facet | Chaos Dynamique réticulaire Golven (algemeen, natuurkunde) Niet-lineaire dynamica Systèmes non linéaires Théories non linéaires Lattice dynamics Nonlinear systems Nonlinear theories Gittermodell Mehrdimensionales System Synergetik Nichtlineares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009638378&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nekorkinvladimiri synergeticphenomenainactivelatticespatternswavessolitonschaos AT velardemanuelg synergeticphenomenainactivelatticespatternswavessolitonschaos |