Download or read book Chaos Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space written by Nikolai Verichev and published by Springer Nature. This book was released on 2020-01-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a wider “range” of motion: There are vibrational and rotational types for cyclic variables, as well as their combinations (rotational-vibrational) if the number of cyclic variables is more than one. The specificity of rotator phase space poses serious challenges in terms of selecting methods for studying the dynamics of related systems. The book chiefly focuses on developing a modified form of the method of averaging, which can be used to study the dynamics of rotators. In general, the book uses the “language” of the qualitative theory of differential equations, point mappings, and the theory of bifurcations, which helps authors to obtain new results on dynamical chaos in systems with few degrees of freedom. In addition, a special section is devoted to the study and classification of dynamic structures that can occur in systems with a large number of interconnected objects, i.e. in lattices of rotators and/or oscillators. Given its scope and format, the book can be used both in lectures and courses on nonlinear dynamics, and in specialized courses on the development and operation of relevant systems that can be represented by a large number of various practical systems: interconnected grids of various mechanical systems, various types of networks including not only mechanical but also biological systems, etc.
Download or read book Nonlinear Wave Dynamics of Materials and Structures written by Holm Altenbach and published by Springer Nature. This book was released on 2020-04-22 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.
Download or read book Further Insights into Oscillation Theory written by Nikolai Verichev and published by Cambridge Scholars Publishing. This book was released on 2021-07-27 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is written for students of universities and postgraduate students specializing in the field of nonlinear dynamics, as well as specialists in various fields of mechanical engineering. It is devoted to the development of original methods, and outlines the results of analytical studies of dynamical chaos, synchronization, and dynamic structures in lattices of coupled rotators. It presents its findings within the context of the phase space of models and by involving methods of the qualitative theory of differential equations, the theory of bifurcations, and qualitative numerical methods.
Download or read book Frontiers in the Study of Chaotic Dynamical Systems with Open Problems written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2011 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.
Download or read book Applications of Chaos and Nonlinear Dynamics in Science and Engineering Vol 3 written by Santo Banerjee and published by Springer. This book was released on 2013-06-12 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This third volume concentrates on reviewing further relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such fluctuation relations and chaotic dynamics in physics, fractals and their applications in epileptic seizures, as well as chaos synchronization. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.
Download or read book Synchronization And Control Of Chaos An Introduction For Scientists And Engineers written by Jesus M Gonzalez-miranda and published by World Scientific. This book was released on 2004-10-12 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive overview of the research and latest developments in the field of the dynamics of coupled and driven chaotic oscillators, aimed at a wide audience. Since 1990, there has been very active research devoted to the field, culminating in a considerable body of knowledge, while active research continues.The results presented in the book will be valuable for scientific analysis and explanation in various different scientific disciplines, with potential applications in medicine and engineering. The contents include a selection of the most basic theoretical results, as well as experiments and applications presented at a mathematical level suited to readers working in non-hard sciences. It will also be of interest to physicists and mathematicians looking for an introduction to the field./a
Download or read book Coupled Phase locked Loops Stability Synchronization Chaos And Communication With Chaos written by Matrosov Valery V and published by World Scientific. This book was released on 2018-08-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern technological, biological, and socioeconomic systems are extremely complex. The study of such systems largely relies on the concepts of competition and cooperation (synchronization). The main approaches to the study of nonlinear dynamics of complex systems are now associated with models of collective dynamics of networks and ensembles, formed by interacting dynamical elements.Unfortunately, the applicability of analytical and qualitative methods of nonlinear dynamics to such complex systems is severely restricted due to the high dimension of phase space. Therefore, studying the simplest models of networks, which are ensembles with a small number of elements, becomes of particular interest. Such models allow to make use of the entire spectrum of analytical, qualitative, and numerical methods of nonlinear dynamics. This book is devoted to the investigation of a kind of such systems, namely small ensembles of coupled, phase-controlled oscillators. Both traditional issues, like synchronization, that are relevant for applications in radio-communications, radio-location, energy, etc., and nontraditional issues of excitation of chaotic oscillations and their possible application in advanced communication systems are addressed.
Download or read book Dynamical Chaos written by Vadim Semenovich Anishchenko and published by World Scientific. This book was released on 1995 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hyperbolic Chaos written by Sergey P. Kuznetsov and published by Springer Science & Business Media. This book was released on 2012-03-20 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Download or read book Dynamical Systems written by Jordan Fleming Blocher and published by . This book was released on 2016 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the synchronization of chaotic systems when the coupling between them contains both time averages and stochastic noise. Our model dynamics are given by the Lorenz equations which are a system of three ordinary differential equations in the variables X, Y and Z. Our theoretical results show that coupling two copies of the Lorenz equations using a feedback control which consists of time averages of the X variable leads to exact synchronization provided the time-averaging window is known and sufficiently small. In the presence of noise the convergence is to within a factor of the variance of the noise. The novelty of our investigation hinges on the analysis of the time averages. We also consider the case when the time-averaging window is not known and show that it is possible to tune the feedback control to recover the size of the time-averaging window. Further numerical computations show that synchronization is more accurate and occurs under much less stringent conditions than our theory requires.
Download or read book An Exploration of Dynamical Systems and Chaos written by John H. Argyris and published by Springer. This book was released on 2015-04-24 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures. "This book will be of valuable help for my lectures" Hermann Haken, Stuttgart "This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg “This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, Germany
Download or read book Chaos Concepts Control and Constructive Use written by Yurii Bolotin and published by Springer. This book was released on 2016-10-24 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.
Download or read book Chaos Noise and Fractals written by E. Roy Pike and published by CRC Press. This book was released on 2020-08-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.
Download or read book Chaos Theory written by Ioannis Dimotikalis and published by World Scientific. This book was released on 2011 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic sound composition using coupled cellular automata / Jaime Serquera and Eduardo R. Miranda -- Efficient large-scale forcing in finite-difference simulations of steady isotropic turbulence / Ryo Onishi, Yuya Baba and Keiko Takahashi -- Rendering statistical significance of information flow measures / Angeliki Papana and Dimitris Kugiumtzis. Complexity theory and physical unification : from microscopic to macroscopic level / G.P. Pavlos [und weitere] -- Regular variation, Paretian distributions, and the interplay of light and heavy tails in the fractality of asymptotic models / Dinis D. Pestana, Sandra M. Aleixo and J. Leonel Rocha -- Tools for investigation of dynamics of DC-DC converters within Matlab/Simulink / Dmitry Pikulin -- Chaos as compositional order / Eleri Angharad Pound -- Beta(p, q)-Cantor sets - determinism and randomness / J. Leonel Rocha, Sandra M. Aleixo and Dinis D. Pestana -- Predicting chaos with second method of Lyapunov / Vladimir B. Ryabov -- Analysis of homoclinic bifurcation in Duffing oscillator under two-frequency excitation : peculiarity of using Melnikov method in combination with averaging technique / Vladimir Ryabov and Kenta Fukushima -- Exploring life expectancy limits : first exit time modeling, parameter analysis and forecasts / Christos H. Skiadas and Charilaos Skiadas -- Composing chaotic music from the letter m / Anastasios D. Sotiropoulos -- On the timbre of chaotic algorithmic sounds / Dimitrios A. Sotiropoulos, Anastasios D. Sotiropoulos and Vaggelis D. Sotiropoulos -- The rainbow effect on composing chaotic algorithmic music / Vaggelis D. Sotiropoulos -- A highly chaotic attractor for a dual-channel single-attractor, private communication system / Banlue Srisuchinwong and Buncha Munmuangsaen -- Manifestation of chaos in collective models of nuclei / Pavel Stransky [und weitere] -- Importance of the chaos for computational processes of collective intelligence in social structures / Tadeusz (Ted) Szuba -- Complex signal generators based on capacitors and on piezoelectric loads / Horia-Nicolai L. Teodorescu and Victor P. Cojocaru -- Drift waves' synchronization by using an external signal. The stabilization of a chaotic plasma turbulence / C.L. Xaplanteris and E. Filippaki -- Chaos game technique as a tool for the analysis of natural geomorphological features / G. Zibret and T. Verbovsek -- Dynamics of a steel turning process / Grzegorz Litak and Rafal Rusinek
Download or read book Engineering Applications of Dynamics of Chaos written by W. Szemplinska-Stupnicka and published by Springer Science & Business Media. This book was released on 1991-12-18 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The treatment of chaotic dynamics in mathematics and physics during last two decades has led to a number of new concepts for the investigation of complex behavior in nonlinear dynamical processes. The aim the CISM course Engineering Applications of Dynamics of Chaos of which this is the proceedings volume was to make these concepts available to engineers and applied scientists possessing only such modest knowledges in mathematics which are usual for engineers, for example graduating from a Technical University. The contents of the articles contributed by leading experts in this field cover not only theoretical foundations and algorithmic and computational aspects but also applications to engineering problems. In the first article an introduction into the basic concepts for the investigation of chaotic behavior of dynamical systems is given which is followed in the second article by an extensive treatment of approximative analytical methods to determine the critical parameter values describing the onset of chaos. The important relation between chaotic dynamics and the phenomenon of turbulence is treated in the third article by studying instabilities various fluid flows. In this contribution also an introduction into interesting phenomenon of pattern formation is given. The fourth and fifth articles present various applications to nonlinear oscillations including roll motions of ships, rattling oscillations in gear boxes, tumbling oscillations of satellites, flutter motions of fluid carrying pipes and vibrations of robot arms. In the final article a short treatment of hyperchaos is given.
Download or read book Chaotic Synchronization written by Erik Mosekilde and published by World Scientific. This book was released on 2002 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the fascinating new concept of chaotic sychronization.
Download or read book Applications of Chaos and Nonlinear Dynamics in Science and Engineering Vol 4 written by Santo Banerjee and published by Springer. This book was released on 2015-05-04 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. his fourth volume concentrates on reviewing further relevant contemporary applications of chaotic and nonlinear dynamics as they apply to the various cuttingedge branches of science and engineering. This encompasses, but is not limited to, topics such as synchronization in complex networks and chaotic circuits, time series analysis, ecological and biological patterns, stochastic control theory and vibrations in mechanical systems. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.
