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Order And Chaos In Nonlinear Physical Systems
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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.
Book Synopsis Order and Chaos in Nonlinear Physical Systems by : Stig Lundqvist
Download or read book Order and Chaos in Nonlinear Physical Systems written by Stig Lundqvist and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a measure of generality. Chaos theory has become a real challenge to physicists with very different interests and also in many other disciplines, of which astronomy, chemistry, medicine, meteorology, economics, and social theory are already embraced at the time of writing. The study of chaos-related phenomena has a truly interdisciplinary charac ter and makes use of important concepts and methods from other disciplines. As one important example, for the description of chaotic structures the branch of mathematics called fractal geometry (associated particularly with the name of Mandelbrot) has proved invaluable. For the discussion of the richness of ordered structures which appear, one relies on the theory of pattern recognition. It is relevant to mention that, to date, computer studies have greatly aided the analysis of theoretical models describing chaos.
Book Synopsis Fractional-Order Nonlinear Systems by : Ivo Petráš
Download or read book Fractional-Order Nonlinear Systems written by Ivo Petráš and published by Springer Science & Business Media. This book was released on 2011-05-30 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.
Book Synopsis Nonlinear Dynamics and Chaos by : J. M. T. Thompson
Download or read book Nonlinear Dynamics and Chaos written by J. M. T. Thompson and published by John Wiley & Sons. This book was released on 2002-02-15 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ein angesehener Bestseller - jetzt in der 2.aktualisierten Auflage! In diesem Buch finden Sie die aktuellsten Forschungsergebnisse auf dem Gebiet nichtlinearer Dynamik und Chaos, einem der am schnellsten wachsenden Teilgebiete der Mathematik. Die seit der ersten Auflage hinzugekommenen Erkenntnisse sind in einem zusätzlichen Kapitel übersichtlich zusammengefasst.
Book Synopsis Variational Principles in Classical Mechanics by : Douglas Cline
Download or read book Variational Principles in Classical Mechanics written by Douglas Cline and published by . This book was released on 2017-08 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two dramatically different philosophical approaches to classical mechanics were developed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These powerful variational formulations have become the preeminent philosophical approach used in modern science, was well as having applications to other fields such as economics and engineering.This book introduces variational principles, and illustrates the intellectual beauty, the remarkable power, and the broad scope, of applying variational principles to classical mechanics. A brief review of Newtonian mechanics compares and contrasts the relative merits of the intuitive Newtonian vectorial formulation, with the more powerful analytical variational formulations. Applications presented cover a wide variety of topics, as well as extensions to accommodate relativistic mechanics, and quantum theory.
Book Synopsis Chaotic Dynamics of Nonlinear Systems by : S. Neil Rasband
Download or read book Chaotic Dynamics of Nonlinear Systems written by S. Neil Rasband and published by Courier Dover Publications. This book was released on 2015-08-19 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the concepts, applications, theory, and technique of chaos. Suitable for advanced undergraduates and graduate students and researchers. Requires familiarity with differential equations and linear vector spaces. 1990 edition.
Book Synopsis Introduction to Applied Nonlinear Dynamical Systems and Chaos by : Stephen Wiggins
Download or read book Introduction to Applied Nonlinear Dynamical Systems and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik
Book Synopsis Chaos and Integrability in Nonlinear Dynamics by : Michael Tabor
Download or read book Chaos and Integrability in Nonlinear Dynamics written by Michael Tabor and published by Wiley-Interscience. This book was released on 1989-01-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial differential equations, and soliton dynamics.
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).
Download or read book Chaos written by Angelo Vulpiani and published by World Scientific. This book was released on 2010 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
Book Synopsis Deterministic Nonlinear Systems by : Vadim S. Anishchenko
Download or read book Deterministic Nonlinear Systems written by Vadim S. Anishchenko and published by Springer. This book was released on 2014-06-16 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
Book Synopsis Nonlinear Dynamics and Chaos by : J Hogan
Download or read book Nonlinear Dynamics and Chaos written by J Hogan and published by CRC Press. This book was released on 2002-08-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such sys
Book Synopsis Chaos and Dynamical Systems by : David P. Feldman
Download or read book Chaos and Dynamical Systems written by David P. Feldman and published by Princeton University Press. This book was released on 2019-08-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
Book Synopsis Student Solutions Manual for Nonlinear Dynamics and Chaos, 2nd edition by : Mitchal Dichter
Download or read book Student Solutions Manual for Nonlinear Dynamics and Chaos, 2nd edition written by Mitchal Dichter and published by CRC Press. This book was released on 2018-05-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the second edition of Steven Strogatz's classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. The textbook and accompanying Student Solutions Manual are aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Complete with graphs and worked-out solutions, this manual demonstrates techniques for students to analyze differential equations, bifurcations, chaos, fractals, and other subjects Strogatz explores in his popular book.
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.
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.
Author :J. A. Tenreiro Machado Publisher :Springer Science & Business Media ISBN 13 :3319014110 Total Pages :433 pages Book Rating :4.3/5 (19 download)
Book Synopsis Discontinuity and Complexity in Nonlinear Physical Systems by : J. A. Tenreiro Machado
Download or read book Discontinuity and Complexity in Nonlinear Physical Systems written by J. A. Tenreiro Machado and published by Springer Science & Business Media. This book was released on 2013-12-04 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed.
