Chaos in nonlinear oscillators: controlling and synchronization
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1996
|
| Schriftenreihe: | [World scientific series on nonlinear science / A]
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 325 S. Ill., graph. Darst. |
| ISBN: | 9810221436 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011013652 | ||
| 003 | DE-604 | ||
| 005 | 19970512 | ||
| 007 | t | ||
| 008 | 961021s1996 ad|| |||| 00||| eng d | ||
| 020 | |a 9810221436 |9 981-02-2143-6 | ||
| 035 | |a (OCoLC)35819992 | ||
| 035 | |a (DE-599)BVBBV011013652 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-91G |a DE-188 | ||
| 050 | 0 | |a QC174.17.C45 | |
| 082 | 0 | |a 003/.85 |2 21 | |
| 084 | |a UG 3900 |0 (DE-625)145629: |2 rvk | ||
| 084 | |a MAT 587f |2 stub | ||
| 084 | |a MAT 496f |2 stub | ||
| 100 | 1 | |a Lakshmanan, M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Chaos in nonlinear oscillators |b controlling and synchronization |c M. Lakshmanan ; K. Murali |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1996 | |
| 300 | |a XII, 325 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a [World scientific series on nonlinear science / A] |v 13 | |
| 650 | 7 | |a Chaos (théorie des systèmes) |2 ram | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 4 | |a Nonlinear oscillators | |
| 700 | 1 | |a Murali, K. |e Verfasser |4 aut | |
| 810 | 2 | |a A] |t [World scientific series on nonlinear science |v 13 |w (DE-604)BV009051753 |9 13 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007372909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007372909 | ||
Datensatz im Suchindex
| _version_ | 1804125503130435584 |
|---|---|
| adam_text | CONTENTS
1. PREFACE v
1. INTRODUCTION 1
1.1 General 1
1.2 Nonlinearity and Chaotic Motions 1
1.3 Dissipative and Conservative Nonlinear Systems 3
1.4 Bifurcations and Chaos Controlling and Synchronization 4
2. LINEAR AND NONLINEAR OSCILLATORS 5
2.1 Linear Oscillators and Predictability 5
2.1.1 Free Oscillations 6
2.1.2 Damped Oscillations 6
2.1.3 Damped and Forced Oscillations: Resonance 9
2.2 Damped and Driven Nonlinear Oscillators 10
2.2.1 Free Oscillations 10
2.2.2 Damped Oscillations 11
2.2.3 Forced Oscillations Primary Resonance and Jump
Phenomenon (Hysteresis) 13
2.2.4 Secondary Resonances (Subharmonic and Superharmonic) 14
2.3 Nonlinear Oscillations and Bifurcations 14
2.4 Dynamical Systems and Chaos 16
2.5 Routes to Chaos 18
3. ELECTRONIC CIRCUITS AS OSCILLATORS AND
ANALOG SIMULATION OF DYNAMICAL SYSTEMS 21
3.1 Linear and Nonlinear Circuit Elements 22
3.2 Linear Circuits 25
3.3 Nonlinear Circuits: Asymptotic Behaviour 29
3.4 Simplest Circuits with a Nonlinear Resistor (Chua s Diode) 30
3.5 Analog Circuit Simulations of Nonlinear Odes 32
ix
x Contents
4. DUFFING OSCILLATOR: BIFURCATION AND CHAOS 35
4.1 Scaling Property and Three dimensional Control Parameter Space 36
4.2 The Double well Oscillator 37
4.2.1 Period doubling Scenario in f space 39
4.2.2 Phase Diagram in (f uj) Space 48
4.3 Single well Duffing Oscillator 53
4.4 Double hump Potential 60
4.5 Analog Simulation and Experimental Verification 62
5. DUFFING OSCILLATOR: ANALYTIC APPROACHES 67
5.1 Theoretical Analysis of Large orbit T periodic Solution
for the Double well Duffing Oscillator 68
5.1.1 Multiple Scale Method and Perturbative Solution for LO 69
5.1.2 Stability of LO Solution 71
5.2 SO Motion in the Double well Duffing Oscillator and Its
Theoretical Analysis 74
5.3 The Melnikov Criterion 78
5.4 Analytic Structure of the Duffing Oscillator 80
5.4.1 Movable Singularities and Nonlinear Dynamical Systems 80
5.4.2 Singularity Clustering in the Duffing Oscillator 82
6. BIFURCATION, CHAOS AND PHASE LOCKING IN
BVP AND DVP OSCILLATORS 91
6.1 The Bonhoeffer van der Pol Oscillator 91
6.1.1 Bifurcations, Chaos and Phase locking in the BVP Oscillator 93
6.1.2 Mode locking and Complete Devil s Staircase Structures 101
6.2 Duffing van der Pol Oscillator 104
6.3 Analytic Structure of the DVP Oscillator 118
6.3.1 Singularity Analysis of the DVP Equation 119
6.3.2 Infinite Sheeted Solution(ISS) Structure 120
7. CHAOTIC OSCILLATORS WITH CHUA S DIODE 127
7.1 Chua s Diode and Its Characteristics 127
7.2 Simple Practical Implementation of Chua s Diode 129
7.3 Autonomous Circuits with Chua s Diode 131
7.3.1 A. Chua s Autonomous Circuit 131
B. Bifurcations and Chaos: R Bifurcation Sequence 133
7.3.2 Chua s Autonomous Oscillator 135
7.4 Non autonomous Circuits with Chua s Diode 139
7.4.1 Simplified Driven Chua s Circuit 139
Contents xi
7.4.2 Fourth order Driven Chua s Circuit 142
7.5 Chaotic Dynamics of the Simplest Dissipative Non Autonomous
Circuit: Murali Lakshmanan Chua(MLC) Circuit 161
7.5.1 Experimental Realization 162
7.5.2 Stability Analysis 163
7.5.3 Explicit Analytical Solutions 164
7.5.4 Experimental and Numerical Studies 165
7.5.5 Chua s Diode with Single Break point and Spiral
Chua s Attractor 172
7.6 Chaotic Dynamics of the Autonomous van der
Pol Duffing (ADVP) Oscillator 175
7.6.1 Special Cases 177
7.6.2 Third order Autonomous DVP (ADVP) Oscillator 179
8. CONTROLLING OF CHAOS 183
8.1 Algorithm for Controlling of Chaos: Feedback and
Non feedback Methods 183
8.1.1 Feedback Controlling Algorithms 184
8.1.2 Non feedback Methods 185
8.2 Controlling in the BVP Oscillator 187
8.2.1 Adaptive Control Algorithm (ACA) to the BVP Oscillator 188
8.2.2 Suppression of Chaos by Parametric Perturbation 193
8.2.3 Effect of Second Periodic Force I97
8.2.4 Stabilization of Unstable Periodic Orbits 199
8.2.5 Controlling of Chaos by Noise 205
8.3 Controlling in Other Oscillators 209
8.3.1 Controlling of Chaos in Chua s Circuit 209
8 3 2 Controlling of Chaos in Driven Chua s Circuit:
Experimental Results
8.3.3 Controlling of Chaos in Duffing Oscillator and MLC Circuit 220
9. SYNCHRONIZED CHAOTIC SYSTEMS AND SECURE
COMMUNICATION
9.1 Pecora and Carroll Method
9.1.1 Drive response Concept
9.1.2 Chaos Synchronization in Chua s Circuit 239
9.1.3 The Synchronized ADVP Oscillator 242
9.1.4 Asymptotic Stability and Lyapunov Function 245
9.1.5 Cascading Synchronized Systems 246
xii Contents
9.2 Method of One way Coupling 248
9.3 Secure Transmission of Signals by Synchronized Chaotic Systems 256
9.4 Chaotic Signal Masking and Transmission of Analog Signals 257
9.4.1 Signal Transmission Through Cascading Synchronization 258
9.4.2 Method of One way Coupling 265
9.5 Chaotic Switching and Digital Signal Communication 272
9.6 Recent Developments in Synchronization of Chaos 275
Appendix A: PERTURBATION AND RELATED APPROXIMATION
METHODS 285
Appendix B: VAN DER POL OSCILLATOR AND CHAOS 289
Appendix C: SOME FURTHER UBIQUITOUS CHAOTIC
OSCILLATORS 295
GLOSSARY 303
REFERENCES 309
INDEX 319
If
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| author_facet | Lakshmanan, M. Murali, K. |
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| discipline | Physik Informatik Mathematik |
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| id | DE-604.BV011013652 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:02:35Z |
| institution | BVB |
| isbn | 9810221436 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007372909 |
| oclc_num | 35819992 |
| open_access_boolean | |
| owner | DE-739 DE-91G DE-BY-TUM DE-188 |
| owner_facet | DE-739 DE-91G DE-BY-TUM DE-188 |
| physical | XII, 325 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | World Scientific |
| record_format | marc |
| series2 | [World scientific series on nonlinear science / A] |
| spelling | Lakshmanan, M. Verfasser aut Chaos in nonlinear oscillators controlling and synchronization M. Lakshmanan ; K. Murali Singapore [u.a.] World Scientific 1996 XII, 325 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier [World scientific series on nonlinear science / A] 13 Chaos (théorie des systèmes) ram Chaotic behavior in systems Nonlinear oscillators Murali, K. Verfasser aut A] [World scientific series on nonlinear science 13 (DE-604)BV009051753 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007372909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lakshmanan, M. Murali, K. Chaos in nonlinear oscillators controlling and synchronization Chaos (théorie des systèmes) ram Chaotic behavior in systems Nonlinear oscillators |
| title | Chaos in nonlinear oscillators controlling and synchronization |
| title_auth | Chaos in nonlinear oscillators controlling and synchronization |
| title_exact_search | Chaos in nonlinear oscillators controlling and synchronization |
| title_full | Chaos in nonlinear oscillators controlling and synchronization M. Lakshmanan ; K. Murali |
| title_fullStr | Chaos in nonlinear oscillators controlling and synchronization M. Lakshmanan ; K. Murali |
| title_full_unstemmed | Chaos in nonlinear oscillators controlling and synchronization M. Lakshmanan ; K. Murali |
| title_short | Chaos in nonlinear oscillators |
| title_sort | chaos in nonlinear oscillators controlling and synchronization |
| title_sub | controlling and synchronization |
| topic | Chaos (théorie des systèmes) ram Chaotic behavior in systems Nonlinear oscillators |
| topic_facet | Chaos (théorie des systèmes) Chaotic behavior in systems Nonlinear oscillators |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007372909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009051753 |
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