Download or read book The Lorenz Attractor Exists written by Warwick Tucker and published by . This book was released on 1998 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Lorenz Equations written by Colin Sparrow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense.
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 Elegant Chaos Algebraically Simple Chaotic Flows written by Julien Clinton Sprott and published by World Scientific. This book was released on 2010-03-22 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos.No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.
Download or read book The Essence Of Chaos written by Flavio Lorenzelli and published by CRC Press. This book was released on 2003-09-02 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field. Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals. As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.
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 Dynamical Systems and Numerical Analysis written by Andrew Stuart and published by Cambridge University Press. This book was released on 1998-11-28 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
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 Three Dimensional Flows written by Vítor Araújo and published by Springer Science & Business Media. This book was released on 2010-06-10 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors present the elements of a general theory for flows on three-dimensional compact boundaryless manifolds, encompassing flows with equilibria accumulated by regular orbits. The book aims to provide a global perspective of this theory and make it easier for the reader to digest the growing literature on this subject. This is not the first book on the subject of dynamical systems, but there are distinct aspects which together make this book unique. Firstly, this book treats mostly continuous time dynamical systems, instead of its discrete counterpart, exhaustively treated in some other texts. Secondly, this book treats all the subjects from a mathematical perspective with proofs of most of the results included. Thirdly, this book is meant to be an advanced graduate textbook and not just a reference book or monograph on the subject. This aspect is reflected in the way the cover material is presented, with careful and complete proofs, and precise references to topics in the book.
Download or read book Attractors Under Discretisation written by Xiaoying Han and published by Springer. This book was released on 2017-08-11 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
Download or read book Invariant Manifolds written by M.W. Hirsch and published by Springer. This book was released on 2006-11-15 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Strategic Theory for the 21st Century The Little Book on Big Strategy written by Harry R. Yarger and published by DIANE Publishing. This book was released on 2006 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Proceedings of the 12th International Congress on Mathematical Education written by Sung Je Cho and published by Springer. This book was released on 2015-02-10 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.
Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
Download or read book Dynamical Systems and Chaos written by Henk Broer and published by Springer Science & Business Media. This book was released on 2010-10-20 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.
Download or read book Deterministic Nonlinear Systems written by Vadim S. Anishchenko and published by Springer. This book was released on 2014-06-16 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
