A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling: theory and experiment
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2013
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| Schlagworte: | |
| Online-Zugang: | kostenfrei https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130423-1127876-0-2 Inhaltsverzeichnis |
| Beschreibung: | 148 S. Ill., graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Hölzel, Robert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling |b theory and experiment |c Robert Hölzel |
| 264 | 1 | |c 2013 | |
| 300 | |a 148 S. |b Ill., graph. Darst. | ||
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| 502 | |a München, Techn. Univ., Diss., 2013 | ||
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Datensatz im Suchindex
| _version_ | 1804150402207186944 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
5
CONTENTS
1. INTRODUCTION 8
2. THEORETICAL BACKGROUND 13
2.1 ASSOCIATIVE NETWORKS 13
2.2 PATTERN RECOGNITION IN A NETWORK OF INDIVIDUALLY COUPLED IDEAL
OSCILLATORS WITH
EQUAL FREQUENCY AND CONSTANT COUPLING 14
2.2.1 INITIALIZATION OF THE NETWORK 14
2.2.2 RECOGNITION OF A DEFECTIVE PATTERN 15
2.3 PATTERN RECOGNITION IN A NETWORK OF GLOBALLY COUPLED IDEAL
OSCILLATORS WITH
DIFFERENT FREQUENCIES AND WEAK TIME-DEPENDENT COUPLING 20
2.3.1 EQUIVALENCE OF WEAK GLOBAL COUPLING DYNAMICS AND STRONG INDIVIDUAL
COUPLING DYNAMICS 20
2.3.2 CHOOSING SUITABLE FREQUENCIES 24
2.4 PHASE SHIFT EQUATIONS FOR NETWORKS OF WEAKLY COUPLED REALISTIC
OSCILLATORS . . 26
2.4.1 GENERAL CASE 26
2.4.2 PHASE SHIFT EQUATIONS FOR A NETWORK OF WEAKLY COUPLED
NEAR-HARMONIC
OSCILLATORS WITH A GLOBAL COUPLING IN ONE VARIABLE 27
3. METHODS 30
3.1 NUMERICAL 30
3.1.1 TIME INTEGRATION OF ODES 30
3.1.2 SIMULATIONS OF CIRCUIT BEHAVIOR WITH SPICE 30
3.1.3 EXTRACTION OF THE PERIOD AND THE PHASE SHIFT FROM WAVEFORM DATA
... 30
3.1.4 EXTRACTION OF THE TOTAL HARMONIC DISTORTION FROM WAVEFORM DATA
.... 32
3.1.5 CURVE FITTING 33
3.2 ELECTRONIC CIRCUITRY 34
3.2.1 CIRCUIT ELEMENTS 34
3.2.2 SUBCIRCUITS 36
3.2.3 VAN DER POL OSCILLATOR 36
3.3 EXPERIMENTAL 40
3.3.1 PHASE RESPONSE CURVE MEASUREMENTS 40
3.3.2 PATTERN RECOGNITION EXPERIMENTS 41
4. THEORETICAL ANALYSIS 45
4.1 PROPERTIES OF THE PATTERN STATES IN RECOGNITION MODE 45
4.1.1 ORTHOGONAL MEMORIZED PATTERNS 46
HTTP://D-NB.INFO/1038117224
IMAGE 2
6
CONTENTS
4.1.2 NON-ORTHOGONAL MEMORIZED PATTERNS 52
4.2 CHANGES OF THE IDEAL DYNAMICS UNDER NON-IDEAL CONDITIONS PRESENT IN
AN
EXPERIMENT 59
4.2.1 CHANGE INDUCED BY PHASE NOISE 61
4.2.2 CHANGE INDUCED BY DISTORTED OSCILLATIONS WITH AMPLITUDE NOISE ....
69
4.2.3 CHANGE INDUCED BY PHASE NOISE IN THE COUPLING FUNCTION 69
4.2.4 CHANGE INDUCED BY A DISTORTED COUPLING FUNCTION WITH AMPLITUDE
NOISE 72
4.2.5 CHANGE INDUCED BY A SMALL SEPARATION OF TIME SCALES 73
4.3 CONSEQUENCES FOR THE SCALABILITY OF THE NETWORK 80
5. DESIGN OF THE EXPERIMENTS 83
5.1 SELECTION OF THE INDIVIDUAL OSCILLATORS 83
5.2 SELECTION OF THE COUPLING MECHANISM 90
5.2.1 COUPLING THROUGH AN EXTERNAL RESISTOR 90
5.2.2 IMPROVED COUPLING THROUGH AN EXTERNAL RESISTOR 92
5.2.3 COUPLING THROUGH ANALOG COMPUTING DEVICES 95
5.3 COMPLETE CIRCUIT 96
5.3.1 PARAMETERS OF THE INDIVIDUAL OSCILLATORS 96
5.3.2 CIRCUIT WITH IMPROVED COUPLING THROUGH AN EXTERNAL RESISTOR 100
5.3.3 CIRCUIT WITH COUPLING THROUGH ANALOG COMPUTING DEVICES 102
5.4 A PHYSICAL PERSPECTIVE: PATTERN RECOGNITION AS THE RESULT OF MINIMAL
ENTROPY
PRODUCTION 103
6. EXPERIMENTAL RESULTS 106
6.1 PATTERN RECOGNITION IN A NETWORK WITH 8 OSCILLATORS 106
6.1.1 NETWORK OF TD-TYPE OSCILLATORS WITH COUPLING THROUGH A VCR 108
6.1.2 NETWORK OF NIC-TYPE OSCILLATORS WITH COUPLING THROUGH A VCR 112
6.1.3 NETWORK OF NIC-TYPE OSCILLATORS WITH COUPLING THROUGH ANALOG COM
PUTING DEVICES 118
6.1.4 DISCUSSION OF THE RESULTS 122
6.2 LONG TERM BEHAVIOUR DURING PATTERN RECOGNITION 127
6.3 THE STABILIZING EFFECT OF PATTERN INITIALIZATION ON FREQUENCY DRIFT
129
7. SUMMARY 132
REFERENCES 135
A APPENDIX 141
A1 TABLE OF REPEATEDLY USED SYMBOLS AND ABBREVIATIONS 141
IMAGE 3
CONTENTS 7
A2 NUMERICAL INTEGRATION EXAMPLE 143
A3 NETLISTS FOR LTSPICELV 146
A3.1 VAN DER POL OSCILLATOR WITH TUNNEL DIODE 147
A3.2 VAN DER POL OSCILLATOR WITH NIC AND GYRATOR 147
|
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| physical | 148 S. Ill., graph. Darst. |
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| spelling | Hölzel, Robert Verfasser aut A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling theory and experiment Robert Hölzel 2013 148 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2013 (DE-588)4113937-9 Hochschulschrift gnd-content Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20130423-1127876-0-2 http://mediatum.ub.tum.de/node?id=1127876 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130423-1127876-0-2 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026018623&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hölzel, Robert A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling theory and experiment |
| subject_GND | (DE-588)4113937-9 |
| title | A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling theory and experiment |
| title_auth | A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling theory and experiment |
| title_exact_search | A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling theory and experiment |
| title_full | A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling theory and experiment Robert Hölzel |
| title_fullStr | A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling theory and experiment Robert Hölzel |
| title_full_unstemmed | A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling theory and experiment Robert Hölzel |
| title_short | A neural network of weakly coupled nonlinear oscillators with a global, time-dependent coupling |
| title_sort | a neural network of weakly coupled nonlinear oscillators with a global time dependent coupling theory and experiment |
| title_sub | theory and experiment |
| topic_facet | Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1127876 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130423-1127876-0-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026018623&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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