Stochastic and chaotic oscillations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1992
|
| Series: | Mathematics and its applications / Soviet series
77 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XII, 500 S. graph. Darst. |
| ISBN: | 0792315308 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stochastic and chaotic oscillations |c by Yu. I. Neimark and P. S. Landa |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1992 | |
| 300 | |a XII, 500 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
SERIES EDITOR S PREFACE v
PREFACE xi
CHAPTER 1
MATHEMATICAL MODELS OF DETERMINISTIC DISCRETE AND
CONTINUOUS DYNAMICAL SYSTEMS 1
1. Simplest typical models of discrete dynamical systems 2
2. Chaotic motions of deterministic dynamical systems 19
3. Simplest mathematical models of continuous dynamical systems 25
4. Discrete version of continuous dynamical systems 31
5. Models for locally active continuous media 37
CHAPTER 2
ORDER AND CHAOS AS TWO GENERAL BASIC TRENDS IN THE
EVOLUTION OF DYNAMICAL SYSTEMS 40
1. Order and chaos: stability and instability 41
2. Time synchronization phenomena 49
3. Spatial and temporal order and chaos 52
CHAPTER 3
STOCHASTICITY TRANSFORMERS, AMPLIFIERS AND
GENERATORS 57
1. Stochasticity transformers 57
2. Stochasticity amplifiers 62
3. Stochasticity generators 70
4. Is the stochasticity of stochastic and chaotic motions of deterministic
dynamical systems real ? 78
viii
CHAPTER 4
BRIEF SURVEY OF STUDIES RELATED TO THE APPEARANCE OF THE
PROBLEM OF CHAOTIC AND STOCHASTIC MOTIONS AND TO
TURBULENCE THEORY 81
CHAPTER 5
LOCAL PHASE PORTRAITS OF THE SIMPLEST STEADY STATE
MOTIONS AND THEIR BIFURCATIONS 97
1. Equilibrium states 97
2. Bifurcations of equilibrium states 103
3. Phase portraits in the vicinity of periodic motions 115
4. Bifurcations of periodic motions 116
5. Toroidal integral manifolds 127
CHAPTER 6
STOCHASTIC AND CHAOTIC ATTRACTORS 132
1. Auxiliary mappings and sequences of point mappings 134
2. Transition from the negative to the positive and investigation of typical
appearance of chaos 145
3. Conditions for the appearance of chaotic and stochastic attractors 173
CHAPTER 7
BIFURCATIONS AND ROUTES TO CHAOS AND STOCHASTICITY 177
1. General description of the tree of possible bifurcations 179
2. Series of bifurcations 183
3. Bifurcations and the stochastic attractor in a Lorenz system 201
4. Bifurcations and the phase portrait of parametrically excited oscillator or
rotator 215
5. On the appearance of chaos and stochasticity in dissipative dynamical
systems 231
ix
CHAPTER 8
QUANTITATIVE CHARACTERISTICS OF STOCHASTIC AND CHAOTIC
MOTIONS. SOME UNIVERSAL PROPERTIES IN ORDER CHAOS AND
INVERSE TRANSITIONS 241
1. Statistical characteristics 241
2. Lyapunov exponents. Dimension and entropy of a stochastic attractor 252
3. Synchronization threshold as a quantitative characteristic of chaotic motions 264
4. Certain universal laws in order chaos transitions, and analogy with phase
transitions 266
CHAPTER 9
EXAMPLES OF MECHANICAL, PHYSICAL, CHEMICAL, AND
BIOLOGICAL SYSTEMS WITH CHAOTIC AND STOCHASTIC
MOTIONS 293
1. Non linear impact negative friction oscillator and other systems with
discontinuous characteristics 293
2. Tunel diode generators 295
3. Non linear oscillators with periodiei external force 298
4. Lorenz equations and other systems of order three 322
5. Action of a harmonic external force on periodic and chaotic oscillation
generators 351
6. Interaction of oscillation generators of various kinds 368
7. Certain discrete models of turbulence 373
8. Examples of models for chemical kinetics 383
9. Systems with delay and other continuous systems 401
10. Stochasticity in quantum systems 430
BIBLIOGRAPHY 443
INDEX 499
|
| any_adam_object | 1 |
| author | Nejmark, Jurij I. Landa, Polina S. |
| author_facet | Nejmark, Jurij I. Landa, Polina S. |
| author_role | aut aut |
| author_sort | Nejmark, Jurij I. |
| author_variant | j i n ji jin p s l ps psl |
| building | Verbundindex |
| bvnumber | BV005455810 |
| classification_rvk | SK 810 SK 820 |
| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)246569963 (DE-599)BVBBV005455810 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005455810 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:29:50Z |
| institution | BVB |
| isbn | 0792315308 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003413630 |
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| physical | XII, 500 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Nejmark, Jurij I. Verfasser aut Stochastičeskie i chaotičeskie kolebanija Stochastic and chaotic oscillations by Yu. I. Neimark and P. S. Landa Dordrecht u.a. Kluwer Acad. Publ. 1992 XII, 500 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 77 Aus dem Russ. übers. Dissipatives System (DE-588)4209641-8 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Zufallsschwingung (DE-588)4132806-1 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Schwingung (DE-588)4053999-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Schwingung (DE-588)4053999-4 s Chaostheorie (DE-588)4009754-7 s DE-604 Dynamisches System (DE-588)4013396-5 s Chaos (DE-588)4191419-3 s Stochastik (DE-588)4121729-9 s Dissipatives System (DE-588)4209641-8 s Zufallsschwingung (DE-588)4132806-1 s DE-188 Landa, Polina S. Verfasser aut Soviet series Mathematics and its applications 77 (DE-604)BV004708148 77 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003413630&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nejmark, Jurij I. Landa, Polina S. Stochastic and chaotic oscillations Dissipatives System (DE-588)4209641-8 gnd Chaos (DE-588)4191419-3 gnd Chaostheorie (DE-588)4009754-7 gnd Zufallsschwingung (DE-588)4132806-1 gnd Stochastik (DE-588)4121729-9 gnd Schwingung (DE-588)4053999-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4209641-8 (DE-588)4191419-3 (DE-588)4009754-7 (DE-588)4132806-1 (DE-588)4121729-9 (DE-588)4053999-4 (DE-588)4013396-5 |
| title | Stochastic and chaotic oscillations |
| title_alt | Stochastičeskie i chaotičeskie kolebanija |
| title_auth | Stochastic and chaotic oscillations |
| title_exact_search | Stochastic and chaotic oscillations |
| title_full | Stochastic and chaotic oscillations by Yu. I. Neimark and P. S. Landa |
| title_fullStr | Stochastic and chaotic oscillations by Yu. I. Neimark and P. S. Landa |
| title_full_unstemmed | Stochastic and chaotic oscillations by Yu. I. Neimark and P. S. Landa |
| title_short | Stochastic and chaotic oscillations |
| title_sort | stochastic and chaotic oscillations |
| topic | Dissipatives System (DE-588)4209641-8 gnd Chaos (DE-588)4191419-3 gnd Chaostheorie (DE-588)4009754-7 gnd Zufallsschwingung (DE-588)4132806-1 gnd Stochastik (DE-588)4121729-9 gnd Schwingung (DE-588)4053999-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dissipatives System Chaos Chaostheorie Zufallsschwingung Stochastik Schwingung Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003413630&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
| work_keys_str_mv | AT nejmarkjuriji stochasticeskieichaoticeskiekolebanija AT landapolinas stochasticeskieichaoticeskiekolebanija AT nejmarkjuriji stochasticandchaoticoscillations AT landapolinas stochasticandchaoticoscillations |