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...

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 -...

Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed...

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 book discusses a fundamental problem of the natural sciences, namely, the observation of physical and biological systems and the principles by which we gain information about these systems. Is it relevant whether the human observer is himself a part of the system in question? What difference does this make to our representation of the physical world? These difficult questions have occupied scientists and philosophers from Decartes to Bell. In the light of recent advances in quantum mechanics and the theory of dynamical systems, there is good reason to tackle these problems afresh. This...

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 gathers most of the lectures and communications presented at the meeting t held in Bordeaux from the 27th to the 29 h of September and entitled "Far from equi- librium: instabilities and structures." This meeting is part of a series of seve- ral other interdisciplinary conferences such as Elmau 1972, London 1974, Dortmund 1976, Elmau 1977, Tokyo 1978. The old science classification scheme proposed by Auguste Comte tends to be eve- ry day a bit more blurred out: one gives here, if needed, one additional illustra- tion of this trend. The three key words "far from equilibrium,"...

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...