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Complexity And Nonlinear Dynamics
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Book Synopsis Nonlinear Dynamics, Chaos, and Complexity by : Dimitri Volchenkov
Download or read book Nonlinear Dynamics, Chaos, and Complexity written by Dimitri Volchenkov and published by Springer Nature. This book was released on 2020-12-14 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).
Book Synopsis Nonlinear Dynamics in Complex Systems by : Armin Fuchs
Download or read book Nonlinear Dynamics in Complex Systems written by Armin Fuchs and published by Springer Science & Business Media. This book was released on 2012-09-22 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified. This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work. “This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.” “With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.” “What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.” (J.A.Scott Kelso, excerpts from the foreword)
Book Synopsis Foundations of Complex Systems by : G. Nicolis
Download or read book Foundations of Complex Systems written by G. Nicolis and published by World Scientific. This book was released on 2007 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, how natural complexity acts as a source of inspiration for progress at the fundamental level.
Book Synopsis Complex and Chaotic Nonlinear Dynamics by : Thierry Vialar
Download or read book Complex and Chaotic Nonlinear Dynamics written by Thierry Vialar and published by Springer Science & Business Media. This book was released on 2009-04-26 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines. Beyond its focus on economics and finance, including for instance the evolution of macroeconomic growth models towards nonlinear structures as well as signal processing applications to stock markets, fundamental parts of the book are devoted to the use of nonlinear dynamics in mathematics, statistics, signal theory and processing. Numerous examples and applications, almost 700 illustrations and numerical simulations based on the use of Matlab make the book an essential reference for researchers and students from many different disciplines who are interested in the nonlinear field. An appendix recapitulates the basic mathematical concepts required to use the book.
Book Synopsis Synchronization in Complex Networks of Nonlinear Dynamical Systems by : Chai Wah Wu
Download or read book Synchronization in Complex Networks of Nonlinear Dynamical Systems written by Chai Wah Wu and published by World Scientific. This book was released on 2007 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Many of the results, which have been obtained fairly recently and have until now not appeared in textbook form, are presented with complete proofs. This text is suitable for graduate-level study or for researchers who would like to be better acquainted with the latest research in this area. Sample Chapter(s). Chapter 1: Introduction (76 KB). Contents: Graphs, Networks, Laplacian Matrices and Algebraic Connectivity; Graph Models; Synchronization in Networks of Nonlinear Continuous-Time Dynamical Systems; Synchronization in Networks of Coupled Discrete-Time Systems; Synchronization in Network of Systems with Linear Dynamics; Agreement and Consensus Problems in Groups of Interacting Agents. Readership: Graduate students and researchers in physics, applied mathematics and engineering.
Book Synopsis Applications of Nonlinear Dynamics by : Visarath In
Download or read book Applications of Nonlinear Dynamics written by Visarath In and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics, ?uidization processes, applied optics, stochastic resonance, ?ocking and ?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the ?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.
Book Synopsis Chaos and Complexity in Psychology by : Stephen J. Guastello
Download or read book Chaos and Complexity in Psychology written by Stephen J. Guastello and published by Cambridge University Press. This book was released on 2008-11-10 with total page 1020 pages. Available in PDF, EPUB and Kindle. Book excerpt: While many books have discussed methodological advances in nonlinear dynamical systems theory (NDS), this volume is unique in its focus on NDS's role in the development of psychological theory. After an introductory chapter covering the fundamentals of chaos, complexity and other nonlinear dynamics, subsequent chapters provide in-depth coverage of each of the specific topic areas in psychology. A concluding chapter takes stock of the field as a whole, evaluating important challenges for the immediate future. The chapters are written by experts in the use of NDS in each of their respective areas, including biological, cognitive, developmental, social, organizational and clinical psychology. Each chapter provides an in-depth examination of theoretical foundations and specific applications and a review of relevant methods. This edited collection represents the state of the art in NDS science across the disciplines of psychology.
Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Author :José António Tenreiro Machado Publisher :Springer Science & Business Media ISBN 13 :146140231X Total Pages :328 pages Book Rating :4.4/5 (614 download)
Book Synopsis Nonlinear and Complex Dynamics by : José António Tenreiro Machado
Download or read book Nonlinear and Complex Dynamics written by José António Tenreiro Machado and published by Springer Science & Business Media. This book was released on 2011-08-28 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.
Book Synopsis Nonlinear Dynamics in Optical Complex Systems by : Kenju Otsuka
Download or read book Nonlinear Dynamics in Optical Complex Systems written by Kenju Otsuka and published by Springer Science & Business Media. This book was released on 2000-04-30 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive volume on nonlinear dynamics and chaos in optical systems. A few books have been published recently, but they summarize applied mathematical methodologies toward understanding of nonlinear dynamics in laser systems with small degrees of freedom focusing on linearized perturbation and bifurcation analyses. In contrast to these publications, this book summarizes nonlinear dynamic problems in optical complex systems possessing large degrees of freedom, systematically featuring our original experimental results and their theoretical treatments. The new concepts introduced in this book will have a wide appeal to audiences involved in a rapidly-growing field of nonlinear dynamics. This book focuses on nonlinear dynamics and cooperative functions in realistic optical complex systems, such as multimode lasers, laser array, coupled nonlinear-element systems, and their applications to optical processing. This book is prepared for graduate students majoring in optical and laser physics, but the generic nature of complex systems described in this book may stimulate researchers in the field of nonlinear dynamics covering different academic areas including applied mathematics, hydrodynamics, celestial mechanics, chemistry, biology, and economics.
Book Synopsis Nonlinear Dynamics and Chaos: Advances and Perspectives by : Marco Thiel
Download or read book Nonlinear Dynamics and Chaos: Advances and Perspectives written by Marco Thiel and published by Springer. This book was released on 2010-05-17 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.
Book Synopsis Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems by : M. Reza Rahimi Tabar
Download or read book Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems written by M. Reza Rahimi Tabar and published by Springer. This book was released on 2019-07-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.
Book Synopsis Chaos and Complexity Theory for Management: Nonlinear Dynamics by : Banerjee, Santo
Download or read book Chaos and Complexity Theory for Management: Nonlinear Dynamics written by Banerjee, Santo and published by IGI Global. This book was released on 2012-11-30 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although chaos theory refers to the existence between seemingly random events, it has been gaining the attention of science, technology and managements fields. The shift from traditional procedures to the dynamics of chaos and complexity theory has resulted in a new element of complexity thinking, allowing for a greater capability for analyzing and understanding key business processes. Chaos and Complexity Theory for Management: Nonlinear Dynamics explores chaos and complexity theory and its relationship with the understanding of natural chaos in the business environment. Utilizing these theories aids in comprehending the development of businesses as a complex adaptive system.
Book Synopsis Chaos, Complexity and Leadership 2020 by : Şefika Şule Erçetin
Download or read book Chaos, Complexity and Leadership 2020 written by Şefika Şule Erçetin and published by Springer Nature. This book was released on 2021-07-30 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyzes a range of new developments in various fields concerning the concepts of chaos and complexity theory. The proceedings of the 7th International Symposium on Chaos, Complexity and Leadership feature newly developed concepts involving various research methodologies for identifying chaos and complexity in different fields of the sciences and leadership. In addition, it explores chaotic and complex systems from all fields of knowledge in order to stake a claim of prevalence of compatibility between knowledge fields. Particular emphasis is placed on exploring non-linearity in order to open a discussion on new approaches to and perspectives on chaos, complexity and leadership. Readers will find coverage of important events that have recently taken place in our world, regardless of whether they were social, political, economic or scientific in nature. The book explores diverse aspects of and issues related to the effects of chaos and complexity in the world; discusses the application of nonlinear dynamics in order to arrive at transformational policies; and offers projections of tomorrow’s world using an interdisciplinary approach. Though primarily intended for readers with an interest in nonlinear science, thanks to its focus on the application of chaos and complexity to other disciplines, the book appeals to a broad readership.
Download or read book Philosophy of Complex Systems written by and published by Elsevier. This book was released on 2011-05-23 with total page 951 pages. Available in PDF, EPUB and Kindle. Book excerpt: The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on.Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years.-Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included
Book Synopsis Self-Organized Biological Dynamics and Nonlinear Control by : Jan Walleczek
Download or read book Self-Organized Biological Dynamics and Nonlinear Control written by Jan Walleczek and published by Cambridge University Press. This book was released on 2006-04-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growing impact of nonlinear science on biology and medicine is fundamentally changing our view of living organisms and disease processes. This book introduces the application to biomedicine of a broad range of interdisciplinary concepts from nonlinear dynamics, such as self-organization, complexity, coherence, stochastic resonance, fractals and chaos. It comprises 18 chapters written by leading figures in the field and covers experimental and theoretical research, as well as the emerging technological possibilities such as nonlinear control techniques for treating pathological biodynamics, including heart arrhythmias and epilepsy. This book will attract the interest of professionals and students from a wide range of disciplines, including physicists, chemists, biologists, sensory physiologists and medical researchers such as cardiologists, neurologists and biomedical engineers.
Book Synopsis From Instability to Intelligence by : Michail Zak
Download or read book From Instability to Intelligence written by Michail Zak and published by Springer Science & Business Media. This book was released on 2008-12-11 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word "instability" in day-to-day language is associated with some thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about "good" instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi bility in thermodynamics, the phenomena of chaos and turbulence in clas sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or "errors" in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.
