Download or read book Chaotic Instabilities and Their Applications written by Dmytro Vavriv and published by . This book was released on 2009 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Instabilities Chaos and Turbulence written by Paul Manneville and published by World Scientific. This book was released on 2010 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.
Download or read book Instabilities and Chaos in Quantum Optics written by F.Tito Arecchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of the variety of nonlinear dynamical systems that exhibit deterministic chaos optical systems both lasers and passive devices provide nearly ideal systems for quantitative investigation due to their simplicity both in construction and in the mathematics that describes them. In view of their growing technical application the understanding, control and possible exploitation of sources of instability in these systems has considerable practical importance. The aim of this volume is to provide a comprehensive coverage of the current understanding of optical instabilities through a series of reviews by leading researchers in the field. The book comprises nine chapters, five on active (laser) systems and four on passive optically bistable systems. Instabilities and chaos in single- (and multi-) mode lasers with homogeneously and broadened gain media are presented and the influence of an injected signal, loss modulation and also feedback of laser output on this behaviour is treated. Both electrically excited and optically pumped gas lasers are considered, and an analysis of dynamical instabilities in the emission from free electron lasers are presented. Instabilities in passive optically bistable systems include a detailed analysis of the global bifurcations and chaos in which transverse effects are accounted for. Experimental verification of degenerative pulsations and chaos in intrinsic bistable systems is described for various optical feedback systems in which atomic and molecular gases and semiconductors are used as the nonlinear media. Results for a hybrid bistable optical system are significant in providing an important test of current understanding of the dynamical behaviour of passive bistable systems.
Download or read book Stability Instability and Chaos written by Paul Glendinning and published by Cambridge University Press. This book was released on 1994-11-25 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.
Download or read book Discrete Chaos written by Saber N. Elaydi and published by CRC Press. This book was released on 2007-11-09 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determi
Download or read book Instabilities Chaos And Turbulence 2nd Edition written by Paul Manneville and published by World Scientific. This book was released on 2010-07-21 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation./a
Download or read book Engineering Applications of Dynamics of Chaos written by W. Szemplinska-Stupnicka and published by Springer. This book was released on 2014-05-04 with total page 325 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 Handbook of Applications of Chaos Theory written by Christos H. Skiadas and published by CRC Press. This book was released on 2017-12-19 with total page 921 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.
Download or read book Experimental Control of Instabilities and Chaos in Fast Dynamical Systems written by David W. Sukow and published by . This book was released on 1997 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Instabilities and Chaos in Quantum Optics II written by N.B. Abraham and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains tutorial papers from the lectures and seminars presented at the NATO Advanced Study Institute on "Instabilities and Chaos in Quantum Optics", held at the "Il Ciocco" Conference Center, Castelvecchio Pascoli, Lucca, Italy, June 28-July 7, 1987. The title of the volume is designated Instabilities and Chaos in Quantum Optics II, because of the nearly coincident publication of a collection of articles on research in this field edited by F.T. Arecchi and R.G. Harrison [Instabilities and Chaos in Quantum Optics, (Springer, Berlin, 1987) 1. That volume provides more detailed information about some of these topics. Together they will serve as a comprehensive and tutorial pair of companion volumes. This school was directed by Prof. Massimo Inguscio, of the Department of Physics, University of Naples, Naples, Italy to whom we express our gratitude on behalf of all lecturers and students. The Scientific Advisory Committee consisted of N.B. Abraham of Bryn Mawr College; F.T. Arecchi of the National Institute of Optics in Florence and the University of Florence, and L.A. Lugiato of the Politechnic Institute of Torino. The school continues the long tradition of Europhysics Summer Schools in Quantum Electronics which have provided instruction and training for young researchers and advanced students working in this field for almost twenty years.
Download or read book Chaos Theory in the Social Sciences written by L. Douglas Kiel and published by University of Michigan Press. This book was released on 2009-11-10 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos Theory in the Social Sciences: Foundations and Applications offers the most recent thinking in applying the chaos paradigm to the social sciences. The book explores the methodological techniques--and their difficulties--for determining whether chaotic processes may in fact exist in a particular instance and examines implications of chaos theory when applied specifically to political science, economics, and sociology. The contributors to the book show that no single technique can be used to diagnose and describe all chaotic processes and identify the strengths and limitations of a variety of approaches. The essays in this volume consider the application of chaos theory to such diverse phenomena as public opinion, the behavior of states in the international arena, the development of rational economic expectations, and long waves. Contributors include Brian J. L. Berry, Thad Brown, Kenyon B. DeGreene, Dimitrios Dendrinos, Euel Elliott, David Harvey, L. Ted Jaditz, Douglas Kiel, Heja Kim, Michael McBurnett, Michael Reed, Diana Richards, J. Barkley Rosser, Jr., and Alvin M. Saperstein. L. Douglas Kiel and Euel W. Elliott are both Associate Professors of Government, Politics, and Political Economy, University of Texas at Dallas.
Download or read book Semiconductor Lasers written by Junji Ohtsubo and published by Springer. This book was released on 2017-05-03 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the fascinating recent advances made concerning the chaos, stability and instability of semiconductor lasers, and discusses their applications and future prospects in detail. It emphasizes the dynamics in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Applications of semiconductor laser chaos, control and noise, and semiconductor lasers are also demonstrated. Semiconductor lasers with new structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are intriguing and promising devices. Current topics include fast physical number generation using chaotic semiconductor lasers for secure communication, development of chaos, quantum-dot semiconductor lasers and quantum-cascade semiconductor lasers, and vertical-cavity surface-emitting lasers. This fourth edition has been significantly expanded to reflect the latest developments. The fundamental theory of laser chaos and the chaotic dynamics in semiconductor lasers are discussed, but also for example the method of self-mixing interferometry in quantum-cascade lasers, which is indispensable in practical applications. Further, this edition covers chaos synchronization between two lasers and the application to secure optical communications. Another new topic is the consistency and synchronization property of many coupled semiconductor lasers in connection with the analogy of the dynamics between synaptic neurons and chaotic semiconductor lasers, which are compatible nonlinear dynamic elements. In particular, zero-lag synchronization between distant neurons plays a crucial role for information processing in the brain. Lastly, the book presents an application of the consistency and synchronization property in chaotic semiconductor lasers, namely a type of neuro-inspired information processing referred to as reservoir computing.
Download or read book Lectures On Dynamical Systems Structural Stability And Their Applications written by Kotik K Lee and published by World Scientific. This book was released on 1992-05-14 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
Download or read book Perturbation Methods Instability Catastrophe and Chaos written by Wenfang Chen and published by World Scientific. This book was released on 1999 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are stated clearly with their limitations and restrictions and are applied to solve examples from various disciplines. The writing style is informal and new ideas are introduced gradually via concepts already familiar to the reader.
Download or read book Stability Instability and Chaos written by Paul Glendinning and published by Cambridge University Press. This book was released on 1994-11-25 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: By providing an introduction to nonlinear differential equations, Dr Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems. The unique treatment that is found in this book will prove to be an essential guide to stability and chaos.
Download or read book Capture Dynamics and Chaotic Motions in Celestial Mechanics written by Edward Belbruno and published by Princeton University Press. This book was released on 2018-06-05 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel. Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed. Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions. Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.
Download or read book Predictability Stability and Chaos in N Body Dynamical Systems written by Archie E. Roy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems". The Institute was the latest in a series held at three-yearly inter vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.
