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...

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...

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 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...

This book is intended to serve as an introduction to the multidisciplinary ?eld of anomalous diffusion in complex systems such as turbulent plasma, convective rolls, zonal ?ow systems, stochastic magnetic ?elds, etc. In spite of its great importance, turbulent transport has received comparatively little treatment in published mo- graphs. This book attempts a comprehensive description of the scaling approach to turbulent diffusion. From the methodological point of view, the book focuses on the general use of correlation estimates, quasilinear equations, and continuous time random walk -...

The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods,...

This text on the interdisciplinary field of synergetics will be of interest to students and scientists in physics, chemistry, mathematics, biology, electrical, civil and mechanical engineering, and other fields. It continues the outline of basic con- cepts and methods presented in my book Synergetics. An Introduction, which has by now appeared in English, Russian, J apanese, Chinese, and German. I have written the present book in such a way that most of it can be read in- dependently of my previous book, though occasionally some knowledge of that book might be useful. But why do these books...

This volume contains most of the invited papers presented at the International Work- shop on Synergetics, Schloss E1mau, Bavaria, May 2 to.May 7, 1977. This workshop fol- lowed an International Symposium on SynergetiGS at Schloss E1mau, 1972, and an Inter- national SUl11l1erschoo1 at Erice, Sicily, 1974. Synergetics is a rather new field of interdisciplinary research which studies the self-organized behavior of systems leading to the formation of structures and func- tionings. Indeed the whole universe seems to be organized, with pronounced structures starting from spiral galaxies down to...

This volume is the record and product of two International Symposia on the Appli- cation of Catastrophe Theory and Topological Concepts in Physics, held in May and December 1978 at the Institute for Information Sciences, University of TUbingen. The May Symposium centered around the conferral of an honorary doctorate upon Professor Rene Thom, Paris, by the Faculty of Physics of the University of TUbingen in recognition of his discovery of universal structure principles and the new di- mension he has added to scientific knowledge by his pioneering work on structural stability and morphogenesis....

This book contains the manuscripts of the papers delivered at the International Sym- posium on Synergetics held at SchloB Elmau, Bavaria, Germany, from April 30 until May 5, 1979. This conference followed several previous ones (Elmau 1972, Sicily 1974, Elmau 1977). This time the subject of the symposium was "pattern formation by dynam- ic systems and pattern recognition." The meeting brought together scientists from such diverse fields as mathematics, physics, chemistry, biology, history as well as experts in the fields of pattern recognition and associative memory. When I started this type...