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New Dynamical Insights On The Global Behavior Of Chaotic Attractors
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Book Synopsis New Dynamical Insights on the Global Behavior of Chaotic Attractors by : Timothy Douglas Jones
Download or read book New Dynamical Insights on the Global Behavior of Chaotic Attractors written by Timothy Douglas Jones and published by . This book was released on 2012 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advisor: Robert Gilmore.
Book Synopsis Chaotic Systems with Multistability and Hidden Attractors by : Xiong Wang
Download or read book Chaotic Systems with Multistability and Hidden Attractors written by Xiong Wang and published by Springer Nature. This book was released on 2021-12-01 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of new articles written by world-leading experts and active researchers to present their recent finding and progress in the new area of chaotic systems and dynamics, regarding emerging subjects of unconventional chaotic systems and their complex dynamics.It guide readers directly to the research front of the new scientific studies. This book is unique of its kind in the current literature, presenting broad scientific research topics including multistability and hidden attractors in unconventional chaotic systems, such as chaotic systems without equilibria, with only stable equilibria, with a curve or a surface of equilibria. The book describes many novel phenomena observed from chaotic systems, such as non-Shilnikov type chaos, coexistence of different types of attractors, and spontaneous symmetry breaking in chaotic systems. The book presents state-of-the-art scientific research progress in the field with both theoretical advances and potential applications. This book is suitable for all researchers and professionals in the areas of nonlinear dynamics and complex systems, including research professionals, physicists, applied mathematicians, computer scientists and, in particular, graduate students in related fields.
Book Synopsis The Theory of Chaotic Attractors by : Brian R. Hunt
Download or read book The Theory of Chaotic Attractors written by Brian R. Hunt and published by Springer Science & Business Media. This book was released on 2004-01-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu ral" invariant measures. We wanted to bring together a coherent collection of readable, interesting, outstanding papers for detailed study and comparison. We hope that this book will allow serious graduate students to hold seminars to study how the research in this field developed. Limitation of space forced us painfully to exclude many excellent, relevant papers, and the resulting choice reflects the interests of the editors. Since James Alan Yorke was born August 3, 1941, we chose to have this book commemorate his sixtieth birthday, honoring his research in this field. The editors are four of his collaborators. We would particularly like to thank Achi Dosanjh (senior editor math ematics), Elizabeth Young (assistant editor mathematics), Joel Ariaratnam (mathematics editorial), and Yong-Soon Hwang (book production editor) from Springer Verlag in New York for their efforts in publishing this book.
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.
Book Synopsis Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 4 by : Santo Banerjee
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.
Book Synopsis Recent Progress in Controlling Chaos by : Miguel Angel Fernández Sanjuán
Download or read book Recent Progress in Controlling Chaos written by Miguel Angel Fernández Sanjuán and published by World Scientific. This book was released on 2010 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This review volume consists an indispensable collection of research papers chronicling the recent progress in controlling chaos. Here, new theoretical ideas, as experimental implementations of controlling chaos, are included, while the applications contained in this volume can be referred to as turbulent magnetized plasmas, chaotic neural networks, modeling city traffic and models of interest in celestial mechanics. Recent Progress in Controlling Chaos provides an excellent broad overview of the subject matter, and will be especially useful for graduate students, researchers and scientists working in the areas of nonlinear dynamics, chaos and complex systems. The authors, world-renowned scientists and prominent experts in the field of controlling chaos, will offer readers through their research works, a fascinating insight into the state-of-the-art technology used in the progress in key techniques and concepts in the field of control.
Book Synopsis Chaotic Evolution and Strange Attractors by : David Ruelle
Download or read book Chaotic Evolution and Strange Attractors written by David Ruelle and published by Cambridge University Press. This book was released on 1989-09-07 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.
Book Synopsis Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives by : Mark Edelman
Download or read book Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives written by Mark Edelman and published by Springer. This book was released on 2017-11-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to, aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.
Book Synopsis The Topology of Chaos by : Robert Gilmore
Download or read book The Topology of Chaos written by Robert Gilmore and published by John Wiley & Sons. This book was released on 2012-04-30 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required to identify and classify a strange attractor can be extracted from experimental data. In its first edition, the Topology of Chaos has been a valuable resource for physicist and mathematicians interested in the topological analysis of dynamical systems. Since its publication in 2002, important theoretical and experimental advances have put the topological analysis program on a firmer basis. This second edition includes relevant results and connects the material to other recent developments. Following significant improvements will be included: * A gentler introduction to the topological analysis of chaotic systems for the non expert which introduces the problems and questions that one commonly encounters when observing a chaotic dynamics and which are well addressed by a topological approach: existence of unstable periodic orbits, bifurcation sequences, multistability etc. * A new chapter is devoted to bounding tori which are essential for achieving generality as well as for understanding the influence of boundary conditions. * The new edition also reflects the progress which had been made towards extending topological analysis to higher-dimensional systems by proposing a new formalism where evolving triangulations replace braids. * There has also been much progress in the understanding of what is a good representation of a chaotic system, and therefore a new chapter is devoted to embeddings. * The chapter on topological analysis program will be expanded to cover traditional measures of chaos. This will help to connect those readers who are familiar with those measures and tests to the more sophisticated methodologies discussed in detail in this book. * The addition of the Appendix with both frequently asked and open questions with answers gathers the most essential points readers should keep in mind and guides to corresponding sections in the book. This will be of great help to those who want to selectively dive into the book and its treatments rather than reading it cover to cover. What makes this book special is its attempt to classify real physical systems (e.g. lasers) using topological techniques applied to real date (e.g. time series). Hence it has become the experimenter?s guidebook to reliable and sophisticated studies of experimental data for comparison with candidate relevant theoretical models, inevitable to physicists, mathematicians, and engineers studying low-dimensional chaotic systems.
Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz
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.
Book Synopsis Dynamical Chaos by : Vadim Semenovich Anishchenko
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.
Book Synopsis Chaos Unveiled by : Barrett Williams
Download or read book Chaos Unveiled written by Barrett Williams and published by Barrett Williams. This book was released on 2024-08-21 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: **Chaos Unveiled An Expedition into the Intricate World of Chaos Theory and Complex Systems** Unlock the mysteries of the universe's most captivating phenomenon with "Chaos Unveiled," an enlightening journey through chaos theory and complex systems. Crafted to engross and educate, this book serves as your definitive guide to understanding the unpredictable nature of the world around us. Dive into **Chapter 1** and explore the humble beginnings of chaos theory and its dramatic evolution into a pivotal scientific discipline. Discover key contributors and the milestones that have defined this groundbreaking field. Move into **Chapter 2**, where the intricate mathematics behind chaos comes to life. Understand nonlinear dynamics, sensitivity to initial conditions, and the enigmatic strange attractors that lead to seemingly random behaviors out of deterministic processes. In **Chapter 3**, delve into the mesmerizing world of fractals and self-similarity. From the beauty of fractal geometry to real-world applications, this chapter is a visual and intellectual feast. **Chapter 4** takes you into fluid dynamics, demystifying the complex phenomena of turbulence, vortices, and the iconic Lorenz attractor that revolutionized weather prediction and modeling. Explore the fascinating roles chaos plays in **biological systems** in **Chapter 5**, from population dynamics and cardiac rhythms to intricate ecosystems and food webs. Unravel the secrets of chaotic behavior in chemical reactions in **Chapter 6**, and discover how these principles govern both simple reactions and the complex chemistry of living organisms. Venture into **economic chaos** in **Chapter 7**, understanding stock market fluctuations, market bubbles, and the unpredictable nature of economic forecasting. The applications of chaos theory in **engineering** are unlocked in **Chapter 8**, revealing insights into control systems, structural analysis, and the ever-evolving field of robotics and machine learning. **Chapter 9** sheds light on chaos in social systems, from human behavior and social networks to the intricacies of urban planning. Experience medical breakthroughs in **Chapter 10**, where chaos theory enhances diagnostics, epidemiology, and our understanding of brain activity. Discover chaos in the vast expanse of **environmental science** and **astronomy** in **Chapters 11 and 12**, exploring climate change, earthquake prediction, orbital mechanics, and cosmic phenomena. **Chapter 13** provides groundbreaking insights into computational approaches, from numerical simulations to data analysis and pattern recognition. Reflect on the **philosophical implications** in **Chapter 14** as you weigh determinism against randomness and ponder the ethical considerations of predictability. Finally, look towards the **future of chaos theory** in **Chapter 15**, exploring emerging research areas, interdisciplinary collaborations, and the bright horizon of unanswered questions and challenges. "Chaos Unveiled" is not merely a book—it's an invitation to explore, question, and understand the beautifully intricate world of chaos theory. Get ready to have your mind expanded and your curiosity ignited!
Book Synopsis Chaos in Nature by : Christophe Letellier
Download or read book Chaos in Nature written by Christophe Letellier and published by World Scientific. This book was released on 2013 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos theory deals with the description of motion (in a general sense) which cannot be predicted in the long term although produced by deterministic system, as well exemplified by meteorological phenomena. It directly comes from the Lunar theory OCo a three-body problem OCo and the difficulty encountered by astronomers to accurately predict the long-term evolution of the Moon using OC NewtonianOCO mechanics. Henri Poincar(r)''s deep intuitions were at the origin of chaos theory. They also led the meteorologist Edward Lorenz to draw the first chaotic attractor ever published. But the main idea consists of plotting a curve representative of the system evolution rather than finding an analytical solution as commonly done in classical mechanics. Such a novel approach allows the description of population interactions and the solar activity as well. Using the original sources, the book draws on the history of the concepts underlying chaos theory from the 17th century to the last decade, and by various examples, show how general is this theory in a wide range of applications: meteorology, chemistry, populations, astrophysics, biomedicine, et
Book Synopsis Chaotic Evolution and Strange Attractors by : David Ruelle
Download or read book Chaotic Evolution and Strange Attractors written by David Ruelle and published by . This book was released on 1989 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.
Book Synopsis A Gallery of Chua Attractors by : Eleonora Bilotta
Download or read book A Gallery of Chua Attractors written by Eleonora Bilotta and published by World Scientific. This book was released on 2008 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos is considered as one of the most important concepts in modern science. It originally appeared only in computer simulation (the famous Lorenz equation of 1963), but this changed with the introduction of Chua's oscillator (1986) — a simple electronic circuit with the ability to generate a vast range of chaotic behaviors. With Chua's circuit, chaos became a physical phenomenon, readily understood and represented in mathematical language. Yet, even so, it is still difficult for the non-specialist to appreciate the full variety of behaviors that the system can produce.This book aims to bridge the gap. A gallery of nearly 900 “chaotic attractors” — some generated by Chua's physical circuit, the majority through computer simulation of the circuit and its generalizations — are illustrated as 3D color images, time series and fast Fourier transform algorithms. For interested researchers, also presented is the information necessary to replicate the behaviors and images. Finally, how the fractal richness can be plied to artistic ends in generating music and interesting sounds is shown; some examples are included in the DVD-ROM which comes with the book.The contents have also appeared in the International Journal of Bifurcation and Chaos (2007).
Book Synopsis Chaos and Complex Systems by : Stavros G. Stavrinides
Download or read book Chaos and Complex Systems written by Stavros G. Stavrinides and published by Springer Nature. This book was released on 2020-02-19 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the “5th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems (CCS).” All Symposia in the series bring together scientists, engineers, economists and social scientists, creating a vivid forum for discussions on the latest insights and findings obtained in the areas of complexity, nonlinear dynamics and chaos theory, as well as their interdisciplinary applications. The scope of the latest Symposium was enriched with a variety of contemporary, interdisciplinary topics, including but not limited to: fundamental theory of nonlinear dynamics, networks, circuits, systems, biology, evolution and ecology, fractals and pattern formation, nonlinear time series analysis, neural networks, sociophysics and econophysics, complexity management and global systems.
Book Synopsis Recent Trends In Chaotic, Nonlinear And Complex Dynamics by : Jan Awrejcewicz
Download or read book Recent Trends In Chaotic, Nonlinear And Complex Dynamics written by Jan Awrejcewicz and published by World Scientific. This book was released on 2021-07-26 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.
