Regular And Chaotic Oscillations
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Regular And Chaotic Oscillations
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Author : Polina S. Landa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-12
Regular And Chaotic Oscillations written by Polina S. Landa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-12 with Mathematics categories.
This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.
Chaotic Oscillations In Mechanical Systems
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Author : Tomasz Kapitaniak
language : en
Publisher: Manchester University Press
Release Date : 1991
Chaotic Oscillations In Mechanical Systems written by Tomasz Kapitaniak and has been published by Manchester University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Health & Fitness categories.
Regular And Chaotic Dynamics
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Author : A.J. Lichtenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Regular And Chaotic Dynamics written by A.J. Lichtenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.
Regular And Chaotic Dynamics
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Author : Allan J. Lichtenberg
language : en
Publisher:
Release Date : 1992-01-01
Regular And Chaotic Dynamics written by Allan J. Lichtenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Hamiltonian systems categories.
Stochastic And Chaotic Oscillations
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Author : Juri I. Neimark
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic And Chaotic Oscillations written by Juri I. Neimark and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is devoted to stochastic and chaotic oscillations in dissipative systems. Chapter 1 deals with mathematical models of deterministic, discrete and distributed dynamical systems. In Chapter 2, the two basic trends of order and chaos are considered. The next three chapters describe stochasticity transformers, amplifiers and generators, turbulence, and phase portraits of steady-state motions and their bifurcations. Chapter 6 treats the topics of stochastic and chaotic attractors, and this is followed by two chapters dealing with routes to chaos and the quantitative characteristics of stochastic and chaotic motions. Finally, Chapter 9, which comprises more than one-third of the book, presents examples of systems having chaotic and stochastic motions drawn from mechanical, physical, chemical and biological systems. The book concludes with a comprehensive bibliography. For mathematicians, physicists, chemists and biologists interested in stochastic and chaotic oscillations in dynamical systems.
Regular And Chaotic Dynamics
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Author : Allan Lichtenberg
language : en
Publisher:
Release Date : 2014-01-15
Regular And Chaotic Dynamics written by Allan Lichtenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Chaos
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Author : Otto E. Rössler
language : en
Publisher: Springer Nature
Release Date : 2020-05-20
Chaos written by Otto E. Rössler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-20 with Science categories.
Written in the 1980s by one of the fathers of chaos theory, Otto E. Rössler, the manuscript presented in this volume eventually never got published. Almost 40 years later, it remains astonishingly at the forefront of knowledge about chaos theory and many of the examples discussed have never been published elsewhere. The manuscript has now been edited by Christophe Letellier - involved in chaos theory for almost three decades himself, as well as being active in the history of sciences - with a minimum of changes to the original text. Finally released for the benefit of specialists and non-specialists alike, this book is equally interesting from the historical and the scientific points of view: an unconventionally modern approach to chaos theory, it can be read as a classic introduction and short monograph as well as a collection of original insights into advanced topics from this field.
Wave Physics
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Author : Stephen Nettel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Wave Physics written by Stephen Nettel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
This textbook gives a detailed explanation of waves and oscillations in classical physics. These classical phenomena are dealt with at a more advanced level than is customary for second-year courses. All aspects of classical wave physics are presented, including the mathematical and physical basis needed for extended understanding. Finally several chapters are devoted to important topics in current wave physics. Special attention is given to nonlinear waves, solitons, chaotic behavior and associated phenomena. The new edition contains improvements such as full development of Greens functions, a broadening of the treatment of wave mechanics and a closer integration with classical mechanics, plus more examples and problems.
Chaotic Instabilities And Their Applications
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Author : Dmytro Vavriv
language : en
Publisher: Cuvillier Verlag
Release Date : 2009-11-18
Chaotic Instabilities And Their Applications written by Dmytro Vavriv and has been published by Cuvillier Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-18 with Technology & Engineering categories.
The phenomenon of chaos, which is arising as noise-like oscillations in deterministic low-dimensional nonlinear system–s, should be treated from two different points of view. First, this effect can create a threat to stability of many practical systems, and it is needed to know conditions for the chaos to arise. Second, chaotic oscillations can be used for the development of various advanced devices, like noise oscillators, random number generators, noise radars, and so on. Both mentioned directions of the chaos study are addressed in this thesis. In this thesis, we present a first attempt to study chaotic instabilities which arise during the transition of pulses via nonlinear circuits. The mathematical model used is a generalized Duffing equation, which is an adequate model to describe stability in a number of electronic, microwave, and optical devices. The simplest physical oscillator which is described by such equation is a RLC-circuit with nonlinear capacitor, or a cavity with nonlinear element or media. Analytical, numerical, and experimental methods have been used in order to determine conditions for chaotic instabilities arising. For example, the application of secondary averaging has enabled us to find resonances which can give rise to chaotic instabilities, and to determine analytical conditions for chaos onset. These conditions have been compared with those obtained from numerical simulations and experimental investigations, and a good correspondence of the obtained results has been detected. The experiments have been performed with a nonlinear RLC circuit forced by a train of RF-pulses with rectangular envelope and with carrier frequency of about 30 MHz. The obtained results indicate that weakly nonlinear oscillators which are stable under harmonic forcing can lose their stability when a train of pulses is applied. The development of the chaotic instabilities takes place due to the interaction of spectral components of the pulse train. It is shown that there is a certain relation between the pulse duration and the pulse period when the threshold for chaos with respect to pulse intensity reaches a minimum value. This value is also lowering with reduced losses in the system and with increased the period of modulation and the nonlinearity parameter. The second part of the thesis is devoted to the application of chaotic oscillations for the development of reliable sources of random sequences. We have presented a proof that chaotic oscillations generated by some nonlinear systems can be used to produce random binary sequences. These sequences pass the tests specified by the US Standard FIPS PUB 140-1/140-2, and this means that they are suitable for cryptographic applications. Generators of random sequences based on deterministic systems with chaotic behaviour, like physical noise sources, can generate truly random sequences in opposite to software generators, which produce pseudorandom cycle samples. We have also determined regularities of the formation of chaotic oscillations, which can be used for the production of random binary sequences. In particular, it has been detected that the areas of existence of chaotic oscillations in the control parameter space are wider as compared to those areas, where random sequences are produced. Hence, not any chaos generation scheme can be used for the production of random sequences. Moreover, it turned out that not any dynamical system with chaotic behavior is suitable for this purpose. For example, the forced pendulum generates sequences which do not pass the tests for randomness. The most possible reason for not passing the tests is related with the presence of intensive spectral components in the power spectrum. However, the presented results of the study of the Lorenz equations and a pendulum equation with delay as well as the Mackey-Glass equation indicate that it is possible to find dynamical systems with chaotic behavior, which generate random sequences in wide areas of their control parameters. The obtained results clearly indicate that deterministic systems with chaotic behavior can be used as generators of random sequences combining the advantages of software random generators and physical noise sources.
Dynamical Chaos
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Author : Vadim Semenovich Anishchenko
language : en
Publisher: World Scientific
Release Date : 1995
Dynamical Chaos written by Vadim Semenovich Anishchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.