Control of homoclinic chaos by weak periodic perturbations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hackensack, N.J. u.a.
World Scientific
2005
|
| Series: | World scientific series on nonlinear science
series A ; 55 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 223 S. Ill. |
| ISBN: | 9812380426 |
Staff View
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| adam_text | |K I WORLD SCIENTIFIC SIBIE50S | * M *»»** A AM U NONLINEAR SCIENCE^
SERI08 A M5S SERIES EDITOR: LEON 0. CHUA CONTROL OF HOMOCLINIC CHHOS BV
WEFLH PERIODIC PERTURBRTIONS RICARDO CHACON UNIVERSITY OF EXTREMADURA,
SPAIN I WORLD SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE * BEIJING *
SHANGHAI * HONGKONG * TAIPEI * CHENNAI CONTENTS PREFACE VII 1
INTRODUCTION 1 1.1 CONTROL OF CHAOTIC DYNAMICAL SYSTEMS 1 1.2
NON-FEEDBACK CONTROL METHODS 2 1.3 CONTROLLING CHAOS BY WEAK PERIODIC
EXCITATIONS 3 1.3.1 ROBUSTNESS AND FLEXIBILITY 3 1.3.2 APPLICABILITY AND
SCOPE 4 1.4 HARMONIC VERSUS NON-HARMONIC EXCITATIONS: THE WAVEFORM
EFFECT ... 4 1.4.1 RESHAPING-INDUCED STRANGE NON-CHAOTIC ATTRACTORS 6
1.4.2 RESHAPING-INDUCED CRISIS PHENOMENA 14 1.4.3 RESHAPING-INDUCED
BASIN BOUNDARY FRACTALITY 15 1.4.4 RESHAPING-INDUCED ESCAPE FROM A
POTENTIAL WELL 16 1.4.5 RESHAPING-INDUCED CONTROL OF DIRECTED TRANSPORT
20 1.4.6 RESHAPING-INDUCED CONTROL OF SYNCHRONIZATION OF COUPLED LIMIT-
CYCLE OSCILLATORS 26 1.5 NOTES AND REFERENCES 27 2 THEORETICAL APPROACH
31 2.1 DISSIPATIVE SYSTEMS VERSUS HAMILTONIAN SYSTEMS 31 2.2 STABILITY
OF PERTURBED LIMIT CYCLES 32 2.3 NON-AUTONOMOUS SECOND-ORDER
DIFFERENTIAL SYSTEMS 34 2.4 BASICS OF MELNIKOV S METHOD 34 2.4.1
ILLUSTRATION: A DAMPED DRIVEN PENDULUM 38 2.5 THE GENERIC MELNIKOV
FUNCTION: DETERMINISTIC CASE 40 2.5.1 SUPPRESSION OF CHAOS 40 2.5.2
ENHANCEMENT OF CHAOS 56 2.5.3 CASE OF NON-SUBHARMONIC RESONANCES 60
2.5.4 THE SPECIAL CASE OF THE MAIN RESONANCE 68 2.6 THE GENERIC MELNIKOV
FUNCTION: THE NOISE EFFECT 80 2.6.1 ADDITIVE NOISE 81 2.6.2
MULTIPLICATIVE NOISE 84 2.7 NOTES AND REFERENCES 85 CONTENTS PHYSICAL
MECHANISMS 91 3.1 ENERGY-BASED APPROACH 91 3.1.1 MOTIVATION 91 3.1.2
GEOMETRICAL RESONANCE 92 3.1.3 AUTORESONANCE 94 3.1.4 STOCHASTIC
RESONANCE 102 3.2 GEOMETRICAL RESONANCE ANALYSIS: CHAOS, STABILITY AND
CONTROL 106 3.2.1 GEOMETRICAL RESONANCE IN A DAMPED PENDULUM SUBJECTED
TO PE- RIODIC PULSES 106 3.2.2 GEOMETRICAL RESONANCE IN AN OVERDAMPED
BISTABLE SYSTEM ... 110 3.2.3 GEOMETRICAL RESONANCE APPROACH TO CONTROL
OF CHAOS BY WEAK PERIODIC PERTURBATIONS 113 3.2.4 GEOMETRICAL RESONANCE
AND GLOBALLY STABLE LIMIT CYCLE IN THE VAN DER POL OSCILLATOR 116 3.2.5
GEOMETRICAL RESONANCE IN SPATIO-TEMPORAL SYSTEMS 119 3.3 NOTES AND
REFERENCES 121 APPLICATIONS: LOW-DIMENSIONAL SYSTEMS 125 4.1 CONTROL OF
CHAOTIC ESCAPE FROM A POTENTIAL WELL 125 4.1.1 MODEL EQUATIONS 126 4.1.2
ESCAPE SUPPRESSION THEOREMS 128 4.1.3 INHIBITION OF THE EROSION OF
NON-ESCAPING BASINS 132 4.1.4 ROLE OF NONLINEAR DISSIPATION 133 4.1.5
ROBUSTNESS OF CHAOTIC ESCAPE CONTROL 136 4.1.6 CASE OF INCOMMENSURATE
ESCAPE-SUPPRESSING EXCITATIONS .... 139 4.2 TAMING CHAOS IN A DRIVEN
JOSEPHSON JUNCTION 144 4.2.1 MODEL EQUATION 144 4.2.2 SUPPRESSION OF
HOMOCLINIC BIFURCATIONS 145 4.2.3 COMPARISON WITH LYAPUNOV EXPONENT
CALCULATIONS 151 4.3 SUPPRESSION OF CHAOS OF CHARGED PARTICLES IN AN
ELECTROSTATIC WAVE PACKET 159 4.3.1 THE THREE WAVE CASE 159 4.3.2 CASE
OF A GENERAL ELECTROSTATIC WAVE PACKET 167 4.4 NOTES AND REFERENCES 177
APPLICATIONS: HIGH-DIMENSIONAL SYSTEMS 181 5.1 CONTROLLING CHAOS IN
CHAOTIC COUPLED OSCILLATORS 181 5.1.1 LOCALIZED CONTROL OF
SPATIO-TEMPORAL CHAOS 181 5.1.2 APPLICATION TO CHAOTIC SOLITONS IN
FRENKEL-KONTOROVA CHAINS . . 184 5.2 CONTROLLING CHAOS IN PARTIAL
DIFFERENTIAL EQUATIONS 190 5.2.1 DAMPED SINE-GORDON EQUATION ADDITIVELY
DRIVEN BY TWO SPATIO- TEMPORAL PERIODIC FIELDS 191 CONTENTS XIII 5.2.2
DAMPED SINE-GORDON EQUATION ADDITIVELY AND PARAMETRICALLY DRIVEN BY TWO
SPATIO-TEMPORAL PERIODIC FIELDS 195 5.2.3 DAMPED SINE-GORDON EQUATION
ADDITIVELY DRIVEN BY TWO TEM- PORAL PERIODIC EXCITATIONS 198 5.2.4
NONLINEAR SCHRODINGER EQUATION SUBJECTED TO DISSIPATIVE AND SPATIALLY
PERIODIC PERTURBATIONS 202 5.2.5 (J A MODEL ADDITIVELY DRIVEN BY TWO
SPATIO-TEMPORAL PERIODIC FIELDS 204 5.2.6 (F 4 MODEL ADDITIVELY AND
PARAMETRICALLY DRIVEN BY TWO SPATIO-TEMPORAL PERIODIC FIELDS 207 5.3
NOTES AND REFERENCES 210 6 FURTHER REMARKS AND OPEN PROBLEMS 213 6.1
OPEN PROBLEMS 213 6.1.1 BEYOND THE MAIN RESONANCE 213 6.1.2
RESHAPING-INDUCED CONTROL 213 6.1.3 AMPLITUDE MODULATION CONTROL 214 6.2
FURTHER APPLICATIONS 216 6.2.1 RATCHET SYSTEMS 216 6.2.2 COUPLED
BOSE-EINSTEIN CONDENSATES 218 6.3 NOTES AND REFERENCES 219
|
| adam_txt |
|K I WORLD SCIENTIFIC SIBIE50S | * M *»»** A AM U NONLINEAR SCIENCE^
SERI08 A M5S SERIES EDITOR: LEON 0. CHUA CONTROL OF HOMOCLINIC CHHOS BV
WEFLH PERIODIC PERTURBRTIONS RICARDO CHACON UNIVERSITY OF EXTREMADURA,
SPAIN I WORLD SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE * BEIJING *
SHANGHAI * HONGKONG * TAIPEI * CHENNAI CONTENTS PREFACE VII 1
INTRODUCTION 1 1.1 CONTROL OF CHAOTIC DYNAMICAL SYSTEMS 1 1.2
NON-FEEDBACK CONTROL METHODS 2 1.3 CONTROLLING CHAOS BY WEAK PERIODIC
EXCITATIONS 3 1.3.1 ROBUSTNESS AND FLEXIBILITY 3 1.3.2 APPLICABILITY AND
SCOPE 4 1.4 HARMONIC VERSUS NON-HARMONIC EXCITATIONS: THE WAVEFORM
EFFECT . 4 1.4.1 RESHAPING-INDUCED STRANGE NON-CHAOTIC ATTRACTORS 6
1.4.2 RESHAPING-INDUCED CRISIS PHENOMENA 14 1.4.3 RESHAPING-INDUCED
BASIN BOUNDARY FRACTALITY 15 1.4.4 RESHAPING-INDUCED ESCAPE FROM A
POTENTIAL WELL 16 1.4.5 RESHAPING-INDUCED CONTROL OF DIRECTED TRANSPORT
20 1.4.6 RESHAPING-INDUCED CONTROL OF SYNCHRONIZATION OF COUPLED LIMIT-
CYCLE OSCILLATORS 26 1.5 NOTES AND REFERENCES 27 2 THEORETICAL APPROACH
31 2.1 DISSIPATIVE SYSTEMS VERSUS HAMILTONIAN SYSTEMS 31 2.2 STABILITY
OF PERTURBED LIMIT CYCLES 32 2.3 NON-AUTONOMOUS SECOND-ORDER
DIFFERENTIAL SYSTEMS 34 2.4 BASICS OF MELNIKOV'S METHOD 34 2.4.1
ILLUSTRATION: A DAMPED DRIVEN PENDULUM 38 2.5 THE GENERIC MELNIKOV
FUNCTION: DETERMINISTIC CASE 40 2.5.1 SUPPRESSION OF CHAOS 40 2.5.2
ENHANCEMENT OF CHAOS 56 2.5.3 CASE OF NON-SUBHARMONIC RESONANCES 60
2.5.4 THE SPECIAL CASE OF THE MAIN RESONANCE 68 2.6 THE GENERIC MELNIKOV
FUNCTION: THE NOISE EFFECT 80 2.6.1 ADDITIVE NOISE 81 2.6.2
MULTIPLICATIVE NOISE 84 2.7 NOTES AND REFERENCES 85 CONTENTS PHYSICAL
MECHANISMS 91 3.1 ENERGY-BASED APPROACH 91 3.1.1 MOTIVATION 91 3.1.2
GEOMETRICAL RESONANCE 92 3.1.3 AUTORESONANCE 94 3.1.4 STOCHASTIC
RESONANCE 102 3.2 GEOMETRICAL RESONANCE ANALYSIS: CHAOS, STABILITY AND
CONTROL 106 3.2.1 GEOMETRICAL RESONANCE IN A DAMPED PENDULUM SUBJECTED
TO PE- RIODIC PULSES 106 3.2.2 GEOMETRICAL RESONANCE IN AN OVERDAMPED
BISTABLE SYSTEM . 110 3.2.3 GEOMETRICAL RESONANCE APPROACH TO CONTROL
OF CHAOS BY WEAK PERIODIC PERTURBATIONS 113 3.2.4 GEOMETRICAL RESONANCE
AND GLOBALLY STABLE LIMIT CYCLE IN THE VAN DER POL OSCILLATOR 116 3.2.5
GEOMETRICAL RESONANCE IN SPATIO-TEMPORAL SYSTEMS 119 3.3 NOTES AND
REFERENCES 121 APPLICATIONS: LOW-DIMENSIONAL SYSTEMS 125 4.1 CONTROL OF
CHAOTIC ESCAPE FROM A POTENTIAL WELL 125 4.1.1 MODEL EQUATIONS 126 4.1.2
ESCAPE SUPPRESSION THEOREMS 128 4.1.3 INHIBITION OF THE EROSION OF
NON-ESCAPING BASINS 132 4.1.4 ROLE OF NONLINEAR DISSIPATION 133 4.1.5
ROBUSTNESS OF CHAOTIC ESCAPE CONTROL 136 4.1.6 CASE OF INCOMMENSURATE
ESCAPE-SUPPRESSING EXCITATIONS . 139 4.2 TAMING CHAOS IN A DRIVEN
JOSEPHSON JUNCTION 144 4.2.1 MODEL EQUATION 144 4.2.2 SUPPRESSION OF
HOMOCLINIC BIFURCATIONS 145 4.2.3 COMPARISON WITH LYAPUNOV EXPONENT
CALCULATIONS 151 4.3 SUPPRESSION OF CHAOS OF CHARGED PARTICLES IN AN
ELECTROSTATIC WAVE PACKET 159 4.3.1 THE THREE WAVE CASE 159 4.3.2 CASE
OF A GENERAL ELECTROSTATIC WAVE PACKET 167 4.4 NOTES AND REFERENCES 177
APPLICATIONS: HIGH-DIMENSIONAL SYSTEMS 181 5.1 CONTROLLING CHAOS IN
CHAOTIC COUPLED OSCILLATORS 181 5.1.1 LOCALIZED CONTROL OF
SPATIO-TEMPORAL CHAOS 181 5.1.2 APPLICATION TO CHAOTIC SOLITONS IN
FRENKEL-KONTOROVA CHAINS . . 184 5.2 CONTROLLING CHAOS IN PARTIAL
DIFFERENTIAL EQUATIONS 190 5.2.1 DAMPED SINE-GORDON EQUATION ADDITIVELY
DRIVEN BY TWO SPATIO- TEMPORAL PERIODIC FIELDS 191 CONTENTS XIII 5.2.2
DAMPED SINE-GORDON EQUATION ADDITIVELY AND PARAMETRICALLY DRIVEN BY TWO
SPATIO-TEMPORAL PERIODIC FIELDS 195 5.2.3 DAMPED SINE-GORDON EQUATION
ADDITIVELY DRIVEN BY TWO TEM- PORAL PERIODIC EXCITATIONS 198 5.2.4
NONLINEAR SCHRODINGER EQUATION SUBJECTED TO DISSIPATIVE AND SPATIALLY
PERIODIC PERTURBATIONS 202 5.2.5 (J A MODEL ADDITIVELY DRIVEN BY TWO
SPATIO-TEMPORAL PERIODIC FIELDS 204 5.2.6 (F 4 MODEL ADDITIVELY AND
PARAMETRICALLY DRIVEN BY TWO SPATIO-TEMPORAL PERIODIC FIELDS 207 5.3
NOTES AND REFERENCES 210 6 FURTHER REMARKS AND OPEN PROBLEMS 213 6.1
OPEN PROBLEMS 213 6.1.1 BEYOND THE MAIN RESONANCE 213 6.1.2
RESHAPING-INDUCED CONTROL 213 6.1.3 AMPLITUDE MODULATION CONTROL 214 6.2
FURTHER APPLICATIONS 216 6.2.1 RATCHET SYSTEMS 216 6.2.2 COUPLED
BOSE-EINSTEIN CONDENSATES 218 6.3 NOTES AND REFERENCES 219 |
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| indexdate | 2024-07-09T20:26:35Z |
| institution | BVB |
| isbn | 9812380426 |
| language | English |
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| physical | XIII, 223 S. Ill. |
| publishDate | 2005 |
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| publisher | World Scientific |
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| series | World scientific series on nonlinear science |
| series2 | World scientific series on nonlinear science : series A |
| spelling | Chacón, Ricardo Verfasser aut Control of homoclinic chaos by weak periodic perturbations Ricardo Chacón Hackensack, N.J. u.a. World Scientific 2005 XIII, 223 S. Ill. txt rdacontent n rdamedia nc rdacarrier World scientific series on nonlinear science : series A 55 Chaotisches System (DE-588)4316104-2 gnd rswk-swf Optimale periodische Kontrolle (DE-588)4199297-0 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Optimale periodische Kontrolle (DE-588)4199297-0 s DE-604 World scientific series on nonlinear science series A ; 55 (DE-604)BV009051753 55 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014171256&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chacón, Ricardo Control of homoclinic chaos by weak periodic perturbations World scientific series on nonlinear science Chaotisches System (DE-588)4316104-2 gnd Optimale periodische Kontrolle (DE-588)4199297-0 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4199297-0 |
| title | Control of homoclinic chaos by weak periodic perturbations |
| title_auth | Control of homoclinic chaos by weak periodic perturbations |
| title_exact_search | Control of homoclinic chaos by weak periodic perturbations |
| title_exact_search_txtP | Control of homoclinic chaos by weak periodic perturbations |
| title_full | Control of homoclinic chaos by weak periodic perturbations Ricardo Chacón |
| title_fullStr | Control of homoclinic chaos by weak periodic perturbations Ricardo Chacón |
| title_full_unstemmed | Control of homoclinic chaos by weak periodic perturbations Ricardo Chacón |
| title_short | Control of homoclinic chaos by weak periodic perturbations |
| title_sort | control of homoclinic chaos by weak periodic perturbations |
| topic | Chaotisches System (DE-588)4316104-2 gnd Optimale periodische Kontrolle (DE-588)4199297-0 gnd |
| topic_facet | Chaotisches System Optimale periodische Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014171256&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009051753 |
| work_keys_str_mv | AT chaconricardo controlofhomoclinicchaosbyweakperiodicperturbations |