Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions.
It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution).
The focus is on relaxation processes in homogeneous...
Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and no...
Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.
Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and h...
When we contemplate phenomena as diverse as electrochemical deposition or the spatial patterns of urban development, it is natural to assume that they havenothing incommon. Afterall, therearemanylevelsinthehierarchythat builds up from atoms to human society, and the rules that govern atoms are quite di?erent from those that govern the geographical emergence of a city. The common view among many, if not most, biologists and social scientists is that the devil is entirely in the details. This school of thought asserts that social science and biology have little or nothing in common, and indeed...
When we contemplate phenomena as diverse as electrochemical deposition or the spatial patterns of urban development, it is natural to assume that they...
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...
We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically,...
Synchronization processes are of great interest and importance in biology, medicine and physics. In particular, for the comprehension of brain function- ing it appears inevitable that one should analyze neuronal synchronization processes. This book presents a new understanding of how a stimulus in- fluences synchronization patterns of a population of oscillators. On the one hand, a variety of stimulation-induced dynamical phenomena will be pre- sented; on the other hand, new data analysis tools will be developed which will serve as a link between theory and experiment. In this way it will be...
Synchronization processes are of great interest and importance in biology, medicine and physics. In particular, for the comprehension of brain functio...
The study of permutation complexity can be envisioned as a new kind of symbolic dynamics. This book is primarily addressed to researchers working in nonlinear dynamics and complex systems. It is also for graduate students interested in these subjects.
The study of permutation complexity can be envisioned as a new kind of symbolic dynamics. This book is primarily addressed to researchers working in n...
Everything the Power of the World does is done in a circle. The sky is round and I have heard that the earth is round like a ball and so are all the stars. The wind, in its greatest power, whirls. Birds make their nests in circles, for theirs is the same religion as ours. The sun comes forth and goes down again in a circle. The moon does the same and both are round. Even the seasons form a great circle in their changing and always come back again to where they were. The life of a man is a circle from childhood to childhood. And so it is everything where power moves. Black Elk (1863-1950)...
Everything the Power of the World does is done in a circle. The sky is round and I have heard that the earth is round like a ball and so are all the s...
This fascinating work is devoted to the fundamental phenomenon in physics - synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced...
This fascinating work is devoted to the fundamental phenomenon in physics - synchronization that occurs in coupled non-linear dissipative oscillato...
This fourth edition of Stochastic Methods is thoroughly revised and augmented, and has been completely reset. While keeping to the spirit of the book I wrote originally, I have reorganised the chapters of Fokker-Planck equations and those on appr- imation methods, and introduced new material on the white noise limit of driven stochastic systems, and on applications and validity of simulation methods based on the Poisson representation. Further, in response to the revolution in ?nancial m- kets following from the discovery by Fischer Black and Myron Scholes of a reliable option pricing...
This fourth edition of Stochastic Methods is thoroughly revised and augmented, and has been completely reset. While keeping to the spirit of the book ...
The first edition of this book has found great interest among scientists and en- gineers dealing with pattern recognition and among psychologists working on psychophysics or Gestalt psychology. This book also proved highly useful for graduate students of informatics. The concept of the synergetic computer offers an important alternative to the by now more traditional neural nets. I just mention a few advantages: There are no ghost states so that time-consuming methods such as simulated annealing can be avoided; the synaptic strengths are explicitly determined by the prototype patterns to be...
The first edition of this book has found great interest among scientists and en- gineers dealing with pattern recognition and among psychologists work...
