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Author : M. R. Frey
Release : 1995
Genre :
Kind : eBook
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Book Synopsis Noise-Induced Transitions to Chaos by : M. R. Frey
Download or read book Noise-Induced Transitions to Chaos written by M. R. Frey. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W. Horsthemke
Release : 2006-09-12
Genre : Science
Kind : eBook
Book Rating : 523/5 ( reviews)
Book Synopsis Noise-Induced Transitions by : W. Horsthemke
Download or read book Noise-Induced Transitions written by W. Horsthemke. This book was released on 2006-09-12. Available in PDF, EPUB and Kindle. Book excerpt: 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 : E. Simiu
Release : 1994
Genre :
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Book Synopsis Transitions to Chaos Induced by Additive and Multiplicative Noise by : E. Simiu
Download or read book Transitions to Chaos Induced by Additive and Multiplicative Noise written by E. Simiu. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W. Horsthemke
Release : 1984
Genre : Mathematics
Kind : eBook
Book Rating : 591/5 ( reviews)
Book Synopsis Noise-Induced Transitions by : W. Horsthemke
Download or read book Noise-Induced Transitions written by W. Horsthemke. This book was released on 1984. Available in PDF, EPUB and Kindle. Book excerpt: This classic text, an often-requested reprint, develops and explains the foundations of noise-induced processes. At its core is a self-contained, textbook-style presentation of the elements of probability theory, of the theory of Markovian diffusion processes and of the theory of stochastic differential equations, on which the modeling of fluctuating natural and artificial environments is based. Following an introduction to the mathematical tools, the occurrence and the properties of noise-induced transitions are then analyzed for rapidly fluctuating environments describable by the white-noise idealization. Subsequently, more realistic and general types of colored noises are considered. Appropriate practical methods for dealing with these situations are developed. The latter part of the book contains applications and experimental studies illustrating the many facets of noise-induced transitions. The following applications are considered in Noise-Induced Transitions: population dynamics, electrical circuits, chemical and photochemical reactions, non-linear optics, and hydrodynamical systems.
Author : Linda Reichl
Release : 2013-04-17
Genre : Science
Kind : eBook
Book Rating : 521/5 ( reviews)
Book Synopsis The Transition to Chaos by : Linda Reichl
Download or read book The Transition to Chaos written by Linda Reichl. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: resonances. Nonlinear resonances cause divergences in conventional perturbation expansions. This occurs because nonlinear resonances cause a topological change locally in the structure of the phase space and simple perturbation theory is not adequate to deal with such topological changes. In Sect. (2.3), we introduce the concept of integrability. A sys tem is integrable if it has as many global constants of the motion as degrees of freedom. The connection between global symmetries and global constants of motion was first proven for dynamical systems by Noether [Noether 1918]. We will give a simple derivation of Noether's theorem in Sect. (2.3). As we shall see in more detail in Chapter 5, are whole classes of systems which are now known to be inte there grable due to methods developed for soliton physics. In Sect. (2.3), we illustrate these methods for the simple three-body Toda lattice. It is usually impossible to tell if a system is integrable or not just by looking at the equations of motion. The Poincare surface of section provides a very useful numerical tool for testing for integrability and will be used throughout the remainder of this book. We will illustrate the use of the Poincare surface of section for classic model of Henon and Heiles [Henon and Heiles 1964].
