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Bibliographic Details
Main Authors:	Nejmark, Jurij I. (Author), Landa, Polina S. (Author)
Format:	Book
Language:	English
Published:	Dordrecht u.a. Kluwer Acad. Publ. 1992
Series:	Mathematics and its applications / Soviet series 77
Subjects:	Dissipatives System Chaos Chaostheorie Zufallsschwingung Stochastik Schwingung Dynamisches System
Links:	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
Item Description:	Aus dem Russ. übers.
Physical Description:	XII, 500 S. graph. Darst.
ISBN:	0792315308

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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
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author	Nejmark, Jurij I. Landa, Polina S.
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isbn	0792315308
language	English
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physical	XII, 500 S. graph. Darst.
publishDate	1992
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publisher	Kluwer Acad. Publ.
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series2	Mathematics and its applications / Soviet series
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

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