dynamics of nonlinear time delay systems springer series in synergetics

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Dynamics Of Nonlinear Time Delay Systems

Author : Muthusamy Lakshmanan
ISBN : 3642149383
Genre : Science
File Size : 84. 70 MB
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Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions. Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.

Complex Time Delay Systems

Author : Fatihcan M. Atay
ISBN : 9783642023286
Genre : Science
File Size : 50. 12 MB
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One of the major contemporary challenges in both physical and social sciences is modeling, analyzing, and understanding the self-organization, evolution, behavior, and eventual decay of complex dynamical systems ranging from cell assemblies to the human brain to animal societies. The multi-faceted problems in this domain require a wide range of methods from various scienti?c disciplines. There is no question that the inclusion of time delays in complex system models considerably enriches the challenges presented by the problems. Although this inclusion often becomes inevitable as real-world applications demand more and more realistic m- els, the role of time delays in the context of complex systems so far has not attracted the interest it deserves. The present volume is an attempt toward ?lling this gap. There exist various useful tools for the study of complex time-delay systems. At the forefront is the mathematical theory of delay equations, a relatively mature ?eld in many aspects, which provides some powerful techniques for analytical inquiries, along with some other tools from statistical physics, graph theory, computer science, dynamical systems theory, probability theory, simulation and optimization software, and so on. Nevertheless, the use of these methods requires a certain synergy to address complex systems problems, especially in the presence of time delays.

Relative Information

Author : Guy Jumarie
ISBN : 9783642840173
Genre : Science
File Size : 70. 80 MB
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For four decades, information theory has been viewed almost exclusively as a theory based upon the Shannon measure of uncertainty and information, usually referred to as Shannon entropy. Since the publication of Shannon's seminal paper in 1948, the theory has grown extremely rapidly and has been applied with varied success in almost all areas of human endeavor. At this time, the Shannon information theory is a well established and developed body of knowledge. Among its most significant recent contributions have been the use of the complementary principles of minimum and maximum entropy in dealing with a variety of fundamental systems problems such as predic tive systems modelling, pattern recognition, image reconstruction, and the like. Since its inception in 1948, the Shannon theory has been viewed as a restricted information theory. It has often been argued that the theory is capable of dealing only with syntactic aspects of information, but not with its semantic and pragmatic aspects. This restriction was considered a v~rtue by some experts and a vice by others. More recently, however, various arguments have been made that the theory can be appropriately modified to account for semantic aspects of in formation as well. Some of the most convincing arguments in this regard are in cluded in Fred Dretske's Know/edge & Flow of Information (The M.LT. Press, Cambridge, Mass., 1981) and in this book by Guy lumarie.

Information And Self Organization

Author : Hermann Haken
ISBN : 9783662078938
Genre : Science
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Complex systems are ubiquitous, and practically all branches of science ranging from physics through chemistry and biology to economics and sociology have to deal with them. In this book we wish to present concepts and methods for dealing with complex systems from a unifying point of view. Therefore it may be of inter est to graduate students, professors and research workers who are concerned with theoretical work in the above-mentioned fields. The basic idea for our unified ap proach sterns from that of synergetics. In order to find unifying principles we shall focus our attention on those situations where a complex system changes its macroscopic behavior qualitatively, or in other words, where it changes its macroscopic spatial, temporal or functional structure. Until now, the theory of synergetics has usually begun with a microscopic or mesoscopic description of a complex system. In this book we present an approach which starts out from macroscopic data. In particular we shall treat systems that acquire their new structure without specific interference from the outside; i. e. systems which are self-organizing. The vehicle we shall use is information. Since this word has several quite different meanings, all of which are important for our purpose, we shall discuss its various aspects. These range from Shannon information, from which all semantics has been exorcised, to the effects of information on receivers and the self-creation of meaning.

Concepts And Models Of A Quantitative Sociology

Author : W. Weidlich
ISBN : 9783642817892
Genre : Science
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While the volumes hitherto published in the Springer Series in Synergetics have been devoted almost exclusively to the self-organized formation of structures in physics, chemistry and biology, the present monograph by Weidlich and Haag deals with the formation of "structures" (or "patterns") in society. At first glance it would seem a daring enterprise to deal with the complex processes in society using concepts and methods first developed in physics. But over the past decade it has been shown that there is a large class of phenomena in a variety of fields to which unifying concepts can be applied. This is particulary true of situations in which a system composed of many parts or individuals acquires a new structure on macroscopic scales. Indeed, this is the definition of synergetics which I formulated more than a decade ago, and which formed the basis of my survey on the profound analogies in the behaviour of complex systems, includ ing those of sociology (H. Haken: Synergetics. An Introduction, Volume 1 of this series). As I have pointed out on many occasions, the universal validity of these concepts is neither accidental nor is it caused by a mere extension of physical rules to other fields, but is instead a consequence of deep-rooted struc tural properties of systems of interacting parts which are due to rigorous mathe maticallaws. Generally speaking, concepts and methods originally used in physics can be applied to sociological phenomena in two ways.

Synchronization

Author : Alexander Balanov
ISBN : 9783540721284
Genre : Science
File Size : 86. 44 MB
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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 nature.

Complexity And Synergetics

Author : Stefan C. Müller
ISBN : 9783319643342
Genre : Technology & Engineering
File Size : 52. 22 MB
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All of us are confronted with complex phenomena occurring in daily life and in the living and inanimate nature surrounding us. Our scientific curiosity strives to unravel the mechanisms at work to create such complexity. Among various approaches to solve this problem, the field of synergetics, developed by Hermann Haken, has proven very successful as a general and interdisciplinary concept for describing and explaining complex phenomena that appear in systems under non-equilibrium conditions. These comprise dynamical states in evolving systems, spatial structure-forming processes, synchronization of states and regulatory mechanisms, and many other examples. The encompassing concepts have been applied to many disciplines, like physics, chemistry, biology, and beyond those also from synergetics to information theory, brain science, economics, and others. Starting from basic methods of complexity research and synergetics, this volume contains thirty contributions on complex systems that exhibit spontaneous pattern formation far from thermal equilibrium. Written by international experts and young researchers assembled under one roof, this volume reflects state of the art research from a variety of scientific fields and disciplines where complexity theory and synergetics are important or even indispensable tools today and in the future.

A Route To Chaos Using Fpgas

Author : Bharathwaj Muthuswamy
ISBN : 9783319181059
Genre : Technology & Engineering
File Size : 79. 57 MB
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The purpose of this introductory book is to couple the teaching of chaotic circuit and systems theory with the use of field programmable gate arrays (FPGAs). As such, it differs from other texts on chaos: first, it puts emphasis on combining theoretical methods, simulation tools and physical realization to help the reader gain an intuitive understanding of the properties of chaotic systems. Second, the "medium" used for physical realization is the FPGA. These devices are massively parallel architectures that can be configured to realize a variety of logic functions. Hence, FPGAs can be configured to emulate systems of differential equations. Nevertheless maximizing the capabilities of an FPGA requires the user to understand the underlying hardware and also FPGA design software. This is achieved by the third distinctive feature of this book: a lab component in each chapter. Here, readers are asked to experiment with computer simulations and FPGA designs, to further their understanding of concepts covered in the book. This text is intended for graduate students in science and engineering interested in exploring implementation of nonlinear dynamical (chaotic) systems on FPGAs.

Advanced Synergetics

Author : Hermann Haken
ISBN : 9783642455537
Genre : Science
File Size : 47. 26 MB
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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 address such a wide audience? Why are instabilities such a common feature, and what do devices and self-organizing systems have in common? Self-organizing systems acquire their structures or functions without specific interference from outside. The differentiation of cells in biology, and the process of evolution are both examples of self-organization. Devices such as the electronic oscillators used in radio transmitters, on the other hand, are man made. But we often forget that in many cases devices function by means of pro cesses which are also based on self-organization. In an electronic oscillator the motion of electrons becomes coherent without any coherent driving force from the outside; the device is constructed in such a way as to permit specific collective motions of the electrons. Quite evidently the dividing line between self-organiz ing systems and man-made devices is not at all rigid.

Complex Hamiltonian Dynamics

Author : Tassos Bountis
ISBN : 9783642273049
Genre : Language Arts & Disciplines
File Size : 47. 31 MB
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This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) research oriented problems provide many opportunities to deepen the reader’s insights into specific aspects of the subject matter. Addressing a broad audience of graduate students, theoretical physicists and applied mathematicians, this text combines the benefits of a reference work with those of a self-study guide for newcomers to the field.

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