Download or read book Regular and Chaotic Oscillations in Pendulum like Systems written by V. V. Matrosov and published by . This book was released on 2000 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Regular and Chaotic Oscillations written by Polina S. Landa and published by Springer Science & Business Media. This book was released on 2012-11-12 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Chaotic Oscillations in Mechanical Systems written by Tomasz Kapitaniak and published by Manchester University Press. This book was released on 1991 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Control of Oscillations and Chaos written by Aleksandr L?vovich Fradkov and published by World Scientific. This book was released on 1998 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.

Download or read book Chaos in Circuits and Systems written by Guanrong Chen and published by World Scientific. This book was released on 2002 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, leading experts present current achievements in the forefront of research in the challenging field of chaos in circuits and systems, with emphasis on engineering perspectives, methodologies, circuitry design techniques, and potential applications of chaos and bifurcation. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this field. It is suitable for readers ranging from graduate students, university professors, laboratory researchers and industrial practitioners to applied mathematicians and physicists in electrical, electronic, mechanical, physical, chemical and biomedical engineering and science.

Download or read book Introduction To Control Of Oscillations And Chaos written by Alexander L Fradkov and published by World Scientific. This book was released on 1998-10-20 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.

Download or read book Resonance And Bifurcation To Chaos In Pendulum written by Albert C J Luo and published by World Scientific. This book was released on 2017-12-15 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system.This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum.

Download or read book Chaotic instabilities and their applications written by Dmytro Vavriv and published by Cuvillier Verlag. This book was released on 2009-11-18 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stochastic and Chaotic Oscillations written by Juri I. Neimark and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Chaotic Pendulum written by Moshe Gitterman and published by World Scientific. This book was released on 2010-09-07 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces. No preliminary knowledge, such as complex mathematical or numerical methods, is required from a reader other than undergraduate courses in mathematical physics. A wide group of researchers, along with students and teachers will, thus, benefit from this definitive book on nonlinear dynamics.

Download or read book Regular and Chaotic Dynamics written by A.J. Lichtenberg and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Simulating Hamiltonian Dynamics written by Benedict Leimkuhler and published by Cambridge University Press. This book was released on 2004 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.

Download or read book The Physics of Chaos in Hamiltonian Systems written by George M. Zaslavsky and published by World Scientific. This book was released on 2007 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to familiarize the reader with the essential properties of the chaotic dynamics of Hamiltonian systems by avoiding specialized mathematical tools, thus making it easily accessible to a broader audience of researchers and students. Unique material on the most intriguing and fascinating topics of unsolved and current problems in contemporary chaos theory is presented. The coverage includes: separatrix chaos; properties and a description of systems with non-ergodic dynamics; the distribution of Poincar‚ recurrences and their role in transport theory; dynamical models of the Maxwell's Demon, the occurrence of persistent fluctuations, and a detailed discussion of their role in the problem underlying the foundation of statistical physics; the emergence of stochastic webs in phase space and their link to space tiling with periodic (crystal type) and aperiodic (quasi-crystal type) symmetries. This second edition expands on pseudochaotic dynamics with weak mixing and the new phenomenon of fractional kinetics, which is crucial to the transport properties of chaotic motion. The book is ideally suited to all those who are actively working on the problems of dynamical chaos as well as to those looking for new inspiration in this area. It introduces the physicist to the world of Hamiltonian chaos and the mathematician to actual physical problems.The material can also be used by graduate students.

Download or read book Transient Chaos written by Ying-Cheng Lai and published by Springer Science & Business Media. This book was released on 2011-02-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this Book is to give an overview, based on the results of nearly three decades of intensive research, of transient chaos. One belief that motivates us to write this book is that, transient chaos may not have been appreciated even within the nonlinear-science community, let alone other scientific disciplines.

Download or read book Seven Tales of the Pendulum written by Gregory L. Baker and published by Oxford University Press. This book was released on 2011-02-24 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pendulum is a unique physical system which exhibits remarkably varied and complex behavior under many different conditions. It is also a system which, in its many manifestations, has left a significant imprint on human thought and culture. Using graphs, figures, and narrative to explain scientific ideas and models, Gregory Baker gives a lucid account of the physics of the pendulum, showing the reader how the context of the pendulum progresses over four centuries from that of a simple system of classical physics, to that of a chaotic system, and eventually to that of a modern quantum system. He also describes its fascinating presence in cultural history, from its role in timekeeping and measurements of the earth to its importance as a literary symbol of doom. Seven 'tales', detailing different important facets of the pendulum, show the exciting diversity of the science of the pendulum, and its untold significance in the history of human intellectual development.

Download or read book Nonlinear Oscillations and Waves in Dynamical Systems written by P.S Landa and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

Download or read book Chaos written by Otto E. Rössler and published by Springer Nature. This book was released on 2020-05-20 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.