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| Author | : Edward Abram Celarier |
| Publisher | : |
| Total Pages | : 438 |
| Release | : 1986 |
| Genre | : |
| ISBN | : |
| Author | : Frank Moss |
| Publisher | : Cambridge University Press |
| Total Pages | : 408 |
| Release | : 2009-08-20 |
| Genre | : Science |
| ISBN | : 9780521118521 |
Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The second volume applies the theory of Volume 1 to the calculation of the influence of noise in a variety of contexts. These include quantum mechanics, condensed matter, noise induced transitions, escape processes and transition probabilities, systems with periodic potentials, discrete nonlinear systems, symmetry-breaking transition, and optics.
| Author | : W. Horsthemke |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 322 |
| Release | : 2006-09-12 |
| Genre | : Science |
| ISBN | : 3540368523 |
The study of phase transitions is among the most fascinating fields in physics. Originally limited to transition phenomena in equilibrium systems, this field has outgrown its classical confines during the last two decades. The behavior of far from equilibrium systems has received more and more attention and has been an extremely active and productive subject of research for physicists, chemists and biologists. Their studies have brought about a more unified vision of the laws which govern self-organization processes of physico-chemical and biological sys tems. A major achievement has been the extension of the notion of phase transi tion to instabilities which occur only in open nonlinear systems. The notion of phase transition has been proven fruitful in apphcation to nonequilibrium ins- bihties known for about eight decades, like certain hydrodynamic instabilities, as well as in the case of the more recently discovered instabilities in quantum optical systems such as the laser, in chemical systems such as the Belousov-Zhabotinskii reaction and in biological systems. Even outside the realm of natural sciences, this notion is now used in economics and sociology. In this monograph we show that the notion of phase transition can be extend ed even further. It apphes also to a new class of transition phenomena which occur only in nonequilibrium systems subjected to a randomly fluctuating en vironment.
| Author | : Tian Ma |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 575 |
| Release | : 2013-11-09 |
| Genre | : Mathematics |
| ISBN | : 1461489636 |
This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields.
| Author | : Frank Moss |
| Publisher | : Cambridge University Press |
| Total Pages | : 410 |
| Release | : 1989-04-06 |
| Genre | : Mathematics |
| ISBN | : 0521352290 |
A specially written review of all areas of noise and nonlinear in natural environments.
| Author | : Frank Moss |
| Publisher | : Cambridge University Press |
| Total Pages | : 426 |
| Release | : 1989 |
| Genre | : Science |
| ISBN | : 9780521352291 |
Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The second volume applies the theory of Volume 1 to the calculation of the influence of noise in a variety of contexts. These include quantum mechanics, condensed matter, noise induced transitions, escape processes and transition probabilities, systems with periodic potentials, discrete nonlinear systems, symmetry-breaking transition, and optics.
| Author | : Vadim S. Anishchenko |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 463 |
| Release | : 2007-07-20 |
| Genre | : Science |
| ISBN | : 3540381686 |
We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.
| Author | : Alexei Zaikin |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
| Author | : Werner Ebeling |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 228 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642710042 |
These Proceedings contain invited lectures presented at the third Interna tional Conference on "Irreversible Processes and Dissipative Structures" in Kiihlungsborn (German Democratic Republic) in March, 1985. These con ferences, the first of which was held in Rostock in 1977 and the second in Berlin in 1982, are devoted to the study of irreversible processes far from thermal equilibrium and to the phenomena of selforganization. The meet ing in Kiihlungsborn brought together some 160 mathematicians, physicists, chemists and biologists from 10 countries, who are all interested in the inter disciplinary field of synergetics. The main topics of the conference were basic concepts of selforganization and evolution, such as entropy, instabilities, nucleation, dissipative struc tures, chaos and turbulence. The contributions cover methods from ther modynamics, the theory of dynamic systems, stochastic and statistic theory, the method of Green's functions, the fluctuation-dissipation theorem, etc. Several problems are studied in more detail, e.g., the kinetics of nucleation especially in finite systems, the dynamics of interfaces, reaction-diffusion sys tems, chemical and biochemical pattern formation and information process ing. Further, several contributions are devoted to the development of the concepts of chaos and turbulence. The editors hope that the contributions collected in this volume will pro vide some new information about the field of selforganization, which is in full development now.
| Author | : Sandeep Vohra |
| Publisher | : World Scientific |
| Total Pages | : 434 |
| Release | : 1992-04-24 |
| Genre | : |
| ISBN | : 9814555223 |
This is the first conference dedicated to the understanding of the experimental aspects of chaotic behavior in several fields and to addressing the emerging areas of data analysis and applications of nonlinear phenomena. Areas covered are data analysis and signal processing techniques, optics, applications of chaotic behavior, magnetism, nonlinear electronic circuits, spatiotemporal chaos, semiconductors, and physiology. Each paper shows real data and what can be done with it. Emphasis is on the manifestation of chaos in real systems, measuring it, analyzing it, and using it in new and unique applications.
