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.

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2005 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Download or read book Dynamic Mode Decomposition written by J. Nathan Kutz and published by SIAM. This book was released on 2016-11-23 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.

Download or read book Nonlinear Dynamics And Chaos written by Nicholas B. Tufillaro and published by Addison Wesley Publishing Company. This book was released on 1992-05-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This essential handbook provides the theoretical and experimental tools necessary to begin researching the nonlinear behavior of mechanical, electrical, optical, and other systems. The book describes several nonlinear systems which are realized by desktop experiments, such as an apparatus showing chaotic string vibrations, an LRC circuit displaying strange scrolling patterns, and a bouncing ball machine illustrating the period doubling route to chaos. Fractal measures, periodic orbit extraction, and symbolic analysis are applied to unravel the chaotic motions of these systems. The simplicity of the examples makes this an excellent book for undergraduate and graduate-level physics and mathematics courses, new courses in dynamical systems, and experimental laboratories.

Download or read book Dissipative Structures and Weak Turbulence written by and published by Academic Press. This book was released on 2014-06-28 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dissipative Structure and Weak Turbulence provides an understanding of the emergence and evolution of structures in macroscopic systems. This book discusses the emergence of dissipative structures. Organized into 10 chapters, this book begins with an overview of the stability of a fluid layer with potentially unstable density stratification in the field of gravity. This text then explains the theoretical description of the dynamics of a given system at a formal level. Other chapters consider several examples of how such simplified models can be derived, complicating the picture progressively to account for other phenomena. This book discusses as well the theory and experiments on plain Rayleigh–Bénard convection by setting first the theoretical frame and deriving the analytical solution of the marginal stability problem. The final chapter deals with building a bridge between chaos as studied in weakly confined systems and more advanced turbulence in the most conventional sense. This book is a valuable resource for physicists.

Download or read book Positive Transfer Operators and Decay of Correlations written by Viviane Baladi and published by World Scientific. This book was released on 2000 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system ?mixes?, i.e. ?forgets? its initial conditions.This book, addressed to mathematicians and mathematical (or mathematically inclined) physicists, shows how the powerful technology of transfer operators, imported from statistical physics, has been used recently to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic systems. Links with dynamical zeta functions are explained.The book is intended for graduate students or researchers entering the field, and the technical prerequisites have been kept to a minimum.

Download or read book Computational Symmetry in Computer Vision and Computer Graphics written by Yanxi Liu and published by Now Publishers Inc. This book was released on 2010 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the arts and sciences, as well as in our daily lives, symmetry has made a profound and lasting impact. Likewise, a computational treatment of symmetry and group theory (the ultimate mathematical formalization of symmetry) has the potential to play an important role in computational sciences. Though the term Computational Symmetry was formally defined a decade ago by the first author, referring to algorithmic treatment of symmetries, seeking symmetry from digital data has been attempted for over four decades. Computational symmetry on real world data turns out to be challenging enough that, after decades of effort, a fully automated symmetry-savvy system remains elusive for real world applications. The recent resurging interests in computational symmetry for computer vision and computer graphics applications have shown promising results. Recognizing the fundamental relevance and potential power that computational symmetry affords, we offer this survey to the computer vision and computer graphics communities. This survey provides a succinct summary of the relevant mathematical theory, a historic perspective of some important symmetry-related ideas, a partial yet timely report on the state of the arts symmetry detection algorithms along with its first quantitative benchmark, a diverse set of real world applications, suggestions for future directions and a comprehensive reference list.

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)

Download or read book Rhythms of the Brain written by G. Buzsáki and published by Oxford University Press. This book was released on 2011 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of mechanisms in the brain that allow complicated things to happen in a coordinated fashion have produced some of the most spectacular discoveries in neuroscience. This book provides eloquent support for the idea that spontaneous neuron activity, far from being mere noise, is actually the source of our cognitive abilities. It takes a fresh look at the coevolution of structure and function in the mammalian brain, illustrating how self-emerged oscillatory timing is the brain's fundamental organizer of neuronal information. The small-world-like connectivity of the cerebral cortex allows for global computation on multiple spatial and temporal scales. The perpetual interactions among the multiple network oscillators keep cortical systems in a highly sensitive "metastable" state and provide energy-efficient synchronizing mechanisms via weak links. In a sequence of "cycles," György Buzsáki guides the reader from the physics of oscillations through neuronal assembly organization to complex cognitive processing and memory storage. His clear, fluid writing-accessible to any reader with some scientific knowledge-is supplemented by extensive footnotes and references that make it just as gratifying and instructive a read for the specialist. The coherent view of a single author who has been at the forefront of research in this exciting field, this volume is essential reading for anyone interested in our rapidly evolving understanding of the brain.

Download or read book Traffic Flow Dynamics written by Martin Treiber and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive and instructive coverage of vehicular traffic flow dynamics and modeling. It makes this fascinating interdisciplinary topic, which to date was only documented in parts by specialized monographs, accessible to a broad readership. Numerous figures and problems with solutions help the reader to quickly understand and practice the presented concepts. This book is targeted at students of physics and traffic engineering and, more generally, also at students and professionals in computer science, mathematics, and interdisciplinary topics. It also offers material for project work in programming and simulation at college and university level. The main part, after presenting different categories of traffic data, is devoted to a mathematical description of the dynamics of traffic flow, covering macroscopic models which describe traffic in terms of density, as well as microscopic many-particle models in which each particle corresponds to a vehicle and its driver. Focus chapters on traffic instabilities and model calibration/validation present these topics in a novel and systematic way. Finally, the theoretical framework is shown at work in selected applications such as traffic-state and travel-time estimation, intelligent transportation systems, traffic operations management, and a detailed physics-based model for fuel consumption and emissions.

Download or read book Structural Stability And Morphogenesis written by Rene Thom and published by CRC Press. This book was released on 2018-03-05 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.

Download or read book Chaos written by Kathleen Alligood and published by Springer. This book was released on 2012-12-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

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

Download or read book Parables for the Virtual written by Brian Massumi and published by Duke University Press. This book was released on 2002-04-09 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the body has been the focus of much contemporary cultural theory, the models that are typically applied neglect the most salient characteristics of embodied existence—movement, affect, and sensation—in favor of concepts derived from linguistic theory. In Parables for the Virtual Brian Massumi views the body and media such as television, film, and the Internet, as cultural formations that operate on multiple registers of sensation beyond the reach of the reading techniques founded on the standard rhetorical and semiotic models. Renewing and assessing William James's radical empiricism and Henri Bergson's philosophy of perception through the filter of the post-war French philosophy of Deleuze, Guattari, and Foucault, Massumi links a cultural logic of variation to questions of movement, affect, and sensation. If such concepts are as fundamental as signs and significations, he argues, then a new set of theoretical issues appear, and with them potential new paths for the wedding of scientific and cultural theory. Replacing the traditional opposition of literal and figural with new distinctions between stasis and motion and between actual and virtual, Parables for the Virtual tackles related theoretical issues by applying them to cultural mediums as diverse as architecture, body art, the digital art of Stelarc, and Ronald Reagan's acting career. The result is an intriguing combination of cultural theory, science, and philosophy that asserts itself in a crystalline and multi-faceted argument.

Download or read book Chemical And Biological Processes In Fluid Flows A Dynamical Systems Approach written by Zoltan Neufeld and published by World Scientific. This book was released on 2009-09-29 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many chemical and biological processes take place in fluid environments in constant motion — chemical reactions in the atmosphere, biological population dynamics in the ocean, chemical reactors, combustion, and microfluidic devices. Applications of concepts from the field of nonlinear dynamical systems have led to significant progress over the last decade in the theoretical understanding of complex phenomena observed in such systems.This book introduces the theoretical approaches for describing mixing and transport in fluid flows. It reviews the basic concepts of dynamical phenomena arising from the nonlinear interactions in chemical and biological systems. The coverage includes a comprehensive overview of recent results on the effect of mixing on spatial structure and the dynamics of chemically and biologically active components in fluid flows, in particular oceanic plankton dynamics./a

Download or read book Turbulence Coherent Structures Dynamical Systems and Symmetry written by Philip Holmes and published by Cambridge University Press. This book was released on 2012-02-23 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.