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| Author | : Milos Marek |
| Publisher | : Cambridge University Press |
| Total Pages | : 384 |
| Release | : 1995-07-20 |
| Genre | : Science |
| ISBN | : 9780521438308 |
This graduate text surveys both the theoretical and experimental aspects of deterministic chaotic behaviour.
| Author | : Gérard Iooss |
| Publisher | : North-Holland |
| Total Pages | : 752 |
| Release | : 1983 |
| Genre | : Science |
| ISBN | : |
| Author | : Heinz Georg Schuster |
| Publisher | : Jacaranda |
| Total Pages | : 306 |
| Release | : 1988 |
| Genre | : Chaotic behavior in systems |
| ISBN | : |
| Author | : G. Iooss (ed) |
| Publisher | : |
| Total Pages | : |
| Release | : |
| Genre | : |
| ISBN | : |
| Author | : Yurii Bolotin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 203 |
| Release | : 2009-08-06 |
| Genre | : Science |
| ISBN | : 3642009379 |
The study of physics has changed in character, mainly due to the passage from the analyses of linear systems to the analyses of nonlinear systems. Such a change began, it goes without saying, a long time ago but the qualitative change took place and boldly evolved after the understanding of the nature of chaos in nonlinear s- tems. The importance of these systems is due to the fact that the major part of physical reality is nonlinear. Linearity appears as a result of the simpli?cation of real systems, and often, is hardly achievable during the experimental studies. In this book, we focus our attention on some general phenomena, naturally linked with nonlinearity where chaos plays a constructive part. The ?rst chapter discusses the concept of chaos. It attempts to describe the me- ing of chaos according to the current understanding of it in physics and mat- matics. The content of this chapter is essential to understand the nature of chaos and its appearance in deterministic physical systems. Using the Turing machine, we formulate the concept of complexity according to Kolmogorov. Further, we state the algorithmic theory of Kolmogorov–Martin-Lof ̈ randomness, which gives a deep understanding of the nature of deterministic chaos. Readers will not need any advanced knowledge to understand it and all the necessary facts and de?nitions will be explained.
| Author | : Tomasz Kapitaniak |
| Publisher | : World Scientific |
| Total Pages | : 250 |
| Release | : 1990-09-21 |
| Genre | : Science |
| ISBN | : 9814506605 |
As in the first edition, the influence of random noise on the chaotic behavior of dissipative dynamical systems is investigated. Problems are illustrated by mechanical examples. This revised and updated edition contains new sections on the summary of probability theory, homoclinic chaos, Melnikov method, routes to chaos, stabilization of period-doubling, and Hopf bifurcation by noise. Some chapters have been rewritten and new examples have been added.
| Author | : Angelo Vulpiani |
| Publisher | : World Scientific |
| Total Pages | : 482 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 9814277665 |
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
| Author | : Stephen H. Kellert |
| Publisher | : University of Chicago Press |
| Total Pages | : 191 |
| Release | : 1994-10-28 |
| Genre | : Science |
| ISBN | : 0226429822 |
Chaos theory has captured scientific and popular attention. What began as the discovery of randomness in simple physical systems has become a widespread fascination with "chaotic" models of everything from business cycles to brainwaves to heart attacks. But what exactly does this explosion of new research into chaotic phenomena mean for our understanding of the world? In this timely book, Stephen Kellert takes the first sustained look at the broad intellectual and philosophical questions raised by recent advances in chaos theory—its implications for science as a source of knowledge and for the very meaning of that knowledge itself.
| Author | : P Cvitanovic |
| Publisher | : Routledge |
| Total Pages | : 783 |
| Release | : 2017-07-12 |
| Genre | : Science |
| ISBN | : 1351406035 |
Nature provides many examples of physical systems that are described by deterministic equations of motion, but that nevertheless exhibit nonpredictable behavior. The detailed description of turbulent motions remains perhaps the outstanding unsolved problem of classical physics. In recent years, however, a new theory has been formulated that succeeds in making quantitative predictions describing certain transitions to turbulence. Its significance lies in its possible application to large classes (often very dissimilar) of nonlinear systems. Since the publication of Universality in Chaos in 1984, progress has continued to be made in our understanding of nonlinear dynamical systems and chaos. This second edition extends the collection of articles to cover recent developments in the field, including the use of statistical mechanics techniques in the study of strange sets arising in dynamics. It concentrates on the universal aspects of chaotic motions, the qualitative and quantitative predictions that apply to large classes of physical systems. Much like the previous edition, this book will be an indispensable reference for researchers and graduate students interested in chaotic dynamics in the physical, biological, and mathematical sciences as well as engineering.
| Author | : A.A. Tsonis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 279 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461533600 |
Based on chaos theory two very important points are clear: (I) random looking aperiodic behavior may be the product of determinism, and (2) nonlinear problems should be treated as nonlinear problems and not as simplified linear problems. The theoretical aspects ofchaos have been presented in great detail in several excellent books published in the last five years or so. However, while the problems associated with applications of the theory-such as dimension and Lyapunov exponentsestimation, chaosand nonlinear pre diction, and noise reduction-have been discussed in workshops and ar ticles, they have not been presented in book form. This book has been prepared to fill this gap between theory and ap plicationsand to assist studentsand scientists wishingto apply ideas from the theory ofnonlinear dynamical systems to problems from their areas of interest. The book is intended to be used as a text for an upper-level undergraduate or graduate-level course, as well as a reference source for researchers. My philosophy behind writing this book was to keep it simple and informative without compromising accuracy. I have made an effort to presentthe conceptsby usingsimplesystemsand step-by-stepderivations. Anyone with an understanding ofbasic differential equations and matrix theory should follow the text without difficulty. The book was designed to be self-contained. When applicable, examples accompany the theory. The reader will notice, however, that in the later chapters specific examples become less frequent. This is purposely done in the hope that individuals will draw on their own ideas and research projects for examples.
