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 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 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 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 Classical Mechanics written by V. B. Bhatia and published by Alpha Science Int'l Ltd.. This book was released on 1997 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers the traditional classical mechanics and then introduces nonlinear oscillations and chaos. These subjects, particularly chaos, have become very important in the recent years and are now being included in courses in Physics and elsewhere. Even within classical mechanics subjects such as nearly circular orbits, virial theorem, anharmonic oscillator and precession and nutation of the earth have been included to make the book suit varied requirements. The book can be adopted for foundation courses on classical mechanics at graduate and post-graduate levels in physics, mathematics and astronomy and wherever else classical mechanics may be a requirement.A large number of problems interspersed throughout the text will induce the students to test the knowledge they had acquired before proceeding further. Another important feature is the appendix which contains some computer programs with essential instructions for solving integrals and differential equations and for plotting phase trajectories and strange attractors on the computer screen so that a student could draw these graphs independently.The short biographical sketches of great scientists and mathematicians who made important contributions to the subject might inspire some readers to look up the detailed biographies to gain some insight the way the science develops.
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 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.
Download or read book Chaos in Nonlinear Oscillators written by Muthusamy Lakshmanan and published by World Scientific. This book was released on 1996 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
Download or read book Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields written by John Guckenheimer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Download or read book Chaotic Oscillators Theory And Applications written by Tomasz Kapitaniak and published by World Scientific. This book was released on 1992-11-30 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Download or read book Regular and Chaotic Dynamics written by Allan J. Lichtenberg and published by . This book was released on 1992-01-01 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Regular and Chaotic Dynamics written by Allan Lichtenberg and published by . This book was released on 2014-01-15 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Wave Physics written by Stephen Nettel and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bifurcation And Chaos In Coupled Oscillators written by Jan Awrejcewicz and published by World Scientific. This book was released on 1991-03-30 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a general methodological approach to investigate complex physical systems presented by the author in a previous book. The nonlinear dynamics of coupled oscillators is investigated numerically and analytically. Three different mechanical, and one biomechanical, examples are used to demonstrate a general systematical approach to the study of dissipative dynamical systems. Many original examples of special chaotic behavior are discussed and illustrated.
