{"title":"Springer Series In Synergetics","description":"\u003cp\u003eExplore the complex world of self-organizing systems with the Springer Series in Synergetics. Dive into groundbreaking research, mathematical models, and interdisciplinary perspectives. 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This is the first textbook written by a well-known expert that provides a modern up-to-date introduction for workers outside statistical physics. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in geophysics and meteorology.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49736945336593,"sku":"NGR9783540308829","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51061051523345,"sku":"NIN9783540308829","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52143212593425,"sku":"NLS9783540308829","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540308822.jpg?v=1751284852"},{"product_id":"information-and-self-organization-book-hermann-haken-9783642069574","title":"Information and Self-Organization","description":"The widespread interest this book has found among professors, scientists and stu­ dents working in a variety of fields has made a new edition necessary. I have used this opportunity to add three new chapters on recent developments. One of the most fascinating fields of modern science is cognitive science which has become a meet­ ing place of many disciplines ranging from mathematics over physics and computer science to psychology. Here, one of the important links between these fields is the concept of information which, however, appears in various disguises, be it as Shan­ non information or as semantic information (or as something still different). So far, meaning seemed to be exorcised from Shannon information, whereas meaning plays a central role in semantic (or as it is sometimes called \"pragmatic\") information. In the new chapter 13 it will be shown, however, that there is an important interplay between Shannon and semantic information and that, in particular, the latter plays a decisive role in the fixation of Shannon information and, in cognitive processes, al­ lows a drastic reduction of that information. A second, equally fascinating and rapidly developing field for mathematicians, computer scientists and physicists is quantum information and quantum computa­ tion. The inclusion of these topics is a must for any modern treatise dealing with in­ formation. 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When such transitions from one state to another take place, fluctuations, i.e., random processes, may play an im­ portant role. Over the past decades it has turned out that the Fokker-Planck equation pro­ vides a powerful tool with which the effects of fluctuations close to transition points can be adequately treated and that the approaches based on the Fokker­ Planck equation are superior to other approaches, e.g., based on Langevin equa­ tions. Quite generally, the Fokker-Planck equation plays an important role in problems which involve noise, e.g., in electrical circuits. For these reasons I am sure that this book will find a broad audience. It pro­ vides the reader with a sound basis for the study of the Fokker-Planck equation and gives an excellent survey of the methods of its solution. The author of this book, Hannes Risken, has made substantial contributions to the development and application of such methods, e.g., to laser physics, diffusion in periodic potentials, and other problems. Therefore this book is written by an experienced practitioner, who has had in mind explicit applications to important problems in the natural sciences and electrical engineering.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50049692041489,"sku":"CIN354061530XG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":50996791836945,"sku":"NIN9783540615309","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52333861929233,"sku":"NLS9783540615309","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":53384223293713,"sku":"CIN354061530XVG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/354061530X.jpg?v=1751253034"},{"product_id":"statistical-physics-of-complex-systems-book-eric-bertin-9783030799489","title":"Statistical Physics of Complex Systems","description":"This third edition of Statistical Physics of Complex Systems has been expanded to provide more examples of applications of concepts and methods from statistical physics to the modeling of complex systems. These include avalanche dynamics in materials, models of social agents like road traffic or wealth repartition, the real space aspects of biological evolution dynamics, propagation phenomena on complex networks, formal neural networks and their connection to constraint satisfaction problems.  This course-tested textbook provides graduate students and non-specialists with a basic understanding of the concepts and methods of statistical physics and demonstrates their wide range of applications to interdisciplinary topics in the field of complex system sciences, including selected aspects of theoretical modeling in biology and the social sciences. It covers topics such as non-conserved particles, evolutionary population dynamics, networks, properties of both individual and coupled simple dynamical systems, and convergence theorems, as well as short appendices that offer helpful hints on how to perform simple stochastic simulations in practice. The original spirit of the book is to remain accessible to a broad, non-specialized readership. 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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 stored, but they can equally well be learned, and the learning procedure allows a classification. Also a precise meaning and function can be attributed to \"hidden variables\". The synergetic computer has found a number of important practical applications in industry. I use the opportunity of this second edition to include a new section on transfor­ mation properties of the equations of the synergetic computer and on the invariance properties of its order parameter equations. 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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 kineticequations. 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.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51061048017169,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51061050900753,"sku":"NIN9783540381648","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52121350603025,"sku":"NLS9783540381648","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540381643.jpg?v=1750967723"},{"product_id":"ambiguity-in-mind-and-nature-book-peter-kruse-9783642784132","title":"Ambiguity in Mind and Nature","description":"Ambiguity in Mind and Nature is the result of cognitive multistability, the phenomenon in which an unchanging stimulus, usually visual, gives rise in the subject to an oscillating perceptual interpretation. 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New advances are achieved by applying concepts such as self-organization, chaos theory and complex systems to the latest results of psychological and neurophysical experiments.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51061067940113,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51061070463249,"sku":"NIN9783642784132","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52622625603857,"sku":"NLS9783642784132","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642784135.jpg?v=1753784646"},{"product_id":"principles-of-brain-functioning-book-hermann-haken-9783642795725","title":"Principles of Brain Functioning","description":"It is increasingly being recognized that the experimental and theoretical study of the complex system brain requires the cooperation of many disciplines, in­ cluding biology, medicine, physics, chemistry, mathematics, computer science, linguistics, and others. In this way brain research has become a truly interdis­ ciplinary endeavor. Indeed, the most important progress is quite often made when different disciplines cooperate. Thus it becomes necessary for scientists to look across the fence surrounding their disciplines. The present book is written precisely in this spirit. It addresses graduate students, professors and scientists in a variety of fields, such as biology, medicine and physics. Be­ yond its mathematical representation the book gives ample space to verbal and pictorial descriptions of the main and, as I believe, fundamental new insights, so that it will be of interest to a general readership, too. I use this opportunity to thank my former students, some of whom are my present co-workers, for their cooperation over many years. Among them I wish to mention in particular M. Bestehorn, L. Borland, H. Bunz, A. Daf­ fertshofer, T. Ditzinger, E. Fischer, A. Fuchs, R. Haas, R. Honlinger, V. Jirsa, M. Neufeld, M. Ossig, D. Reimann, M. Schanz, G. Schoner, P. Tass, C. Uhl. My particular thanks go to R. Friedrich and A. Wunderlin for their constant help in many respects. 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At the same time it demonstrates the progress made in this interdisciplinary field. While in the early days of Synergetics, the self­ organized coherent action of atoms in the laser - a physical device - was in the foreground of interest (cf. my book Synergetics: An Introduction (Springer, Berlin, Heidelberg, New York 1977)), the coherent action of nerve cells got into the focus of research, as is witnessed by the book by P. Tass in this series (P. Tass, Phase Resetting in Medicine and Biology (Springer, Berlin, Heidel­ berg, New York 1999)). In these books the elements were disturbed by noise. Now, in the present book by Mikhailov and Calenbuhr, the self-organized coherent action of otherwise chaotic elements is studied and important as well as surprising results by Kaneko, Mikhailov and others are presented. Let me mention just another highly interesting problem treated in this book: the coherent interaction of tens of thousands of reactions going on in biological cells. But other phenomena, such as the formation of swarms of fish or the collective behavior of ants, are also modelled. 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The book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51062656598289,"sku":"NIN9783540712688","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52594257887505,"sku":"NLS9783540712688","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540712682.jpg?v=1750999669"},{"product_id":"nonlinear-world-book-yoshitsugu-oono-9784431540281","title":"The Nonlinear World","description":"The most important characteristic of the “world filled with nonlinearity” is the existence of scale interference: disparate space–time scales interfere with each other. Thus, the effects of unknowable scales invade the world that we can observe directly. 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The author also wishes the book to be helpful to those who have been observing the world, but who wish to appreciate it afresh from a different angle.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51064461492497,"sku":"","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51064463589649,"sku":"NIN9784431540281","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52598459007249,"sku":"NLS9784431540281","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/4431540288.jpg?v=1751417133"},{"product_id":"dissipative-solitons-in-reaction-diffusion-systems-book-andreas-liehr-9783642312502","title":"Dissipative Solitons in Reaction Diffusion Systems","description":"Why writing a book about a specialized task of the large topic of complex systems? And who will read it? 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Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. 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Leading experts and advanced students in math­ ematics, physics, chemistry and computer science met to present and discuss their most recent results in an informal seminar. These were the circumstances that led to the idea of compiling some of the essential contributions presented at this seminar together with others describing basic features of \"optimal struc­ tures in heterogeneous reaction systems\". The aim of this book is to present the scientific results of the intensive work carried out in each of the specific fields of research. Each contribution therefore presents the current state of the art together with a deeper treatment enabling a more comprehensive understanding of that particular field of work. The common ideas which unite all the different contributions are already ex­ pressed in the title of this book. The nature of heterogeneous reaction systems is quite varied. An example is provided by the chemical systems such as noble metal particles which may act as heterogeneous catalysts for gaseous chemical compounds. Under these circumstances the metal particles and\/or their sur­ faces may undergo phase transitions during reaction. 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However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. 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Much new material has been included in the sections dealing with intermittency in birth-death models and noise-induced phase transi- tions. A new section on control of chaotic behavior has been added to Chap. 6. The subtitle of the volume has been changed to better reflect its contents. We acknowledge stimulating discussions with H. Haken and E. Scholl and are grateful to our colleagues M. Bar, D. Battogtokh, M. Eiswirth, M. Hildebrand, K. Krischer, and V. Tereshko for their comments and assistance. We thank M. Lubke for her help in producing new figures for this volume. Berlin and Moscow A. s. Mikhailov April 1996 A. Yu. Loskutov Preface to the First Edition This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. 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