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 : 44. 52 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 : 37. 66 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.

A Route To Chaos Using Fpgas

Author : Bharathwaj Muthuswamy
ISBN : 9783319181059
Genre : Technology & Engineering
File Size : 28. 4 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.

Complexity And Synergetics

Author : Stefan C. Müller
ISBN : 9783319643342
Genre : Technology & Engineering
File Size : 30. 34 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.

Nonlinear Resonances

Author : Shanmuganathan Rajasekar
ISBN : 9783319248868
Genre : Science
File Size : 84. 44 MB
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This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.

Selforganization In Complex Systems The Past Present And Future Of Synergetics

Author : Günter Wunner
ISBN : 9783319276359
Genre : Technology & Engineering
File Size : 33. 93 MB
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This proceedings volume contains talks and poster presentations from the International Symposium "Self-Organization in Complex Systems: The Past, Present, and Future of Synergetics", which took place at Hanse-Wissenschaftskolleg, an Institute of Advanced Studies, in Delmenhorst, Germany, during the period November 13 - 16, 2012. The Symposium was organized in honour of Hermann Haken, who celebrated his 85th birthday in 2012. With his fundamental theory of Synergetics he had laid the mathematical-physical basis for describing and analyzing self-organization processes in a diversity of fields of research. The quest for common and universal principles of self-organization in complex systems was clearly covered by the wide range of interdisciplinary topics reported during the Symposium. These extended from complexity in classical systems and quantum systems over self-organisation in neuroscience even to the physics of finance. Moreover, by combining a historical view with a present status report the Symposium conveyed an impression of the allure and potency of this branch of research as well as its applicability in the future.

Synergetics Of Measurement Prediction And Control

Author : Igor Grabec
ISBN : 9783642603365
Genre : Science
File Size : 34. 54 MB
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In this monograph, a statistical description of natural phenomena is used to develop an information processing system capable of modeling non-linear relationships between sensory data. The system, based on self-organized, optimal preservation of empirical information, applies these relationships for prediction and adaptive control. This monograph is written for students, scientists and engineers in academia and industry who are interested in experimental work related to the adaptive modeling of natural laws, the development of sensory-neural networks, intelligent control, synergetics and informatics. No specific knowledge of advanced mathematics is presupposed. Examples taken from physics, engineering, medicine and economics demonstrate the applicability of such intelligent systems.

Physics Of The Human Mind

Author : Ihor Lubashevsky
ISBN : 9783319517063
Genre : Science
File Size : 32. 95 MB
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This book tackles the challenging question which mathematical formalisms and possibly new physical notions should be developed for quantitatively describing human cognition and behavior, in addition to the ones already developed in the physical and cognitive sciences. Indeed, physics is widely used in modeling social systems, where, in particular, new branches of science such as sociophysics and econophysics have arisen. However, many if not most characteristic features of humans like willingness, emotions, memory, future prediction, and moral norms, to name but a few, are not yet properly reflected in the paradigms of physical thought and theory. The choice of a relevant formalism for modeling mental phenomena requires the comprehension of the general philosophical questions related to the mind-body problem. Plausible answers to these questions are investigated and reviewed, notions and concepts to be used or to be taken into account are developed and some challenging questions are posed as open problems. This text addresses theoretical physicists and neuroscientists modeling any systems and processes where human factors play a crucial role, philosophers interested in applying philosophical concepts to the construction of mathematical models, and the mathematically oriented psychologists and sociologists, whose research is fundamentally related to modeling mental processes.

Control Of Self Organizing Nonlinear Systems

Author : Eckehard Schöll
ISBN : 9783319280288
Genre : Science
File Size : 58. 45 MB
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The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.

Nonlinear Oscillations And Waves In Dynamical Systems

Author : P.S Landa
ISBN : 9789401587631
Genre : Mathematics
File Size : 44. 99 MB
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A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

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