Nonlinear Dynamics and Chaos

With Applications to Physics, Biology, Chemistry, and Engineering

Author: Steven H. Strogatz

Publisher: Westview Press

ISBN: 0813349117

Category: Mathematics

Page: 500

View: 6181

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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. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.

Nonlinear Dynamics and Chaos

With Applications to Physics, Biology, Chemistry, and Engineering

Author: Steven H. Strogatz

Publisher: Hachette UK

ISBN: 0813349117

Category: Mathematics

Page: 500

View: 7384

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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. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.

Chaos and Nonlinear Dynamics

An Introduction for Scientists and Engineers

Author: Robert C. Hilborn,Amanda and Lisa Cross Professor of Physics Robert Hilborn

Publisher: Oxford University Press on Demand

ISBN: 9780198507239

Category: Mathematics

Page: 650

View: 6892

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This is a comprehensive introduction to the exciting scientific field of nonlinear dynamics for students, scientists, and engineers, and requires only minimal prerequisites in physics and mathematics. The book treats all the important areas in the field and provides an extensive and up-to-date bibliography of applications in all fields of science, social science, economics, and even the arts.

Nonlinear Dynamics and Chaos, 2nd ed. SET with Student Solutions Manual

Author: Steven H. Strogatz

Publisher: Westview Press

ISBN: 9780813350844

Category: Mathematics

Page: 932

View: 6799

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Steven H. Strogatz's Nonlinear Dynamics and Chaos, second edition, 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. The Student Solutions Manual, by Mitchal Dichter, includes solutions to the odd-numbered exercises featured in Nonlinear Dynamics and Chaos, second edition. Complete with graphs and worked-out solutions, the Student Solutions Manual demonstrates techniques for students to analyze differential equations, bifurcations, chaos, fractals, and other subjects explored in Strogatz's popular book.

An Introduction To Chaotic Dynamical Systems

Author: Robert Devaney

Publisher: CRC Press

ISBN: 0429981937

Category: Science

Page: 360

View: 7509

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The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.

Chaos

An Introduction to Dynamical Systems

Author: Kathleen Alligood,Tim Sauer,J.A. Yorke

Publisher: Springer

ISBN: 3642592813

Category: Mathematics

Page: 603

View: 3265

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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.

The Joy of X

A Guided Tour of Math, from One to Infinity

Author: Steven Henry Strogatz

Publisher: Houghton Mifflin Harcourt

ISBN: 0547517653

Category: MATHEMATICS

Page: 316

View: 5081

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A comprehensive tour of leading mathematical ideas by an award-winning professor and columnist for the New York Times Opinionator series demonstrates how math intersects with philosophy, science and other aspects of everyday life. By the author of The Calculus of Friendship. 50,000 first printing.

Understanding Nonlinear Dynamics

Author: Daniel Kaplan,Leon Glass

Publisher: Springer Science & Business Media

ISBN: 1461208238

Category: Mathematics

Page: 420

View: 3764

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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.

Dynamics Of Complex Systems

Author: Yaneer Bar-yam

Publisher: Westview Press

ISBN: 9780813341217

Category: Science

Page: 864

View: 6757

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The study of complex systems in a unified framework has become recognized in recent years as a new scientific discipline, the ultimate in the interdisciplinary fields. Breaking down the barriers between physics, chemistry, and biology and the so-called soft sciences of psychology, sociology, economics and anthropology, this text explores the universal physical and mathematical principles that govern the emergence of complex systems from simple components. Dynamics of Complex Systems is the first text describing the modern unified study of complex systems. It is designed for upper-undergraduate/beginning graduate level students, and covers a broad range of applications in a broad array of disciplines. A central goal of this text is to develop models and modeling techniques that are useful when applied to all complex systems. This is done by adopting both analytic tools, including statistical mechanics and stochastic dynamics, and computer simulation techniques, such as cellular automata and Monte Carlo. In four sets of paired, self-contained chapters, Yaneer Bar-Yam discusses complex systems in the context of neural networks, protein folding, living organisms, and finally, human civilization itself. He explores fundamental questions about the structure, dynamics, evolution, development and quantitative complexity that apply to all complex systems. In the first chapter, mathematical foundations such as iterative maps and chaos, probability theory and random walks, thermodynamics, information and computation theory, fractals and scaling, are reviewed to enable the text to be read by students and researchers with a variety of backgrounds.

Introduction to Applied Nonlinear Dynamical Systems and Chaos

Author: Stephen Wiggins

Publisher: Springer Science & Business Media

ISBN: 1475740670

Category: Mathematics

Page: 672

View: 370

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This volume is an introduction to applied nonlinear dynamics and chaos. The emphasis is 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 an extensive bibliography and a detailed glossary of terms.

Nonlinear Dynamics and Chaos

Author: J. M. T. Thompson,Michael Thompson,H. B. Stewart

Publisher: John Wiley & Sons

ISBN: 9780471876847

Category: Mathematics

Page: 437

View: 9344

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Nonlinear dynamics and chaos involves the study of apparent randomhappenings within a system or process. The subject has wideapplications within mathematics, engineering, physics and otherphysical sciences. Since the bestselling first edition waspublished, there has been a lot of new research conducted in thearea of nonlinear dynamics and chaos. * Expands on the bestselling, highly regarded first edition * A new chapter which will cover the new research in the area sincefirst edition * Glossary of terms and a bibliography have been added * All figures and illustrations will be 'modernised' * Comprehensive and systematic account of nonlinear dynamics andchaos, still a fast-growing area of applied mathematics * Highly illustrated * Excellent introductory text, can be used for an advancedundergraduate/graduate course text

Sync

How Order Emerges from Chaos In the Universe, Nature, and Daily Life

Author: Steven H. Strogatz

Publisher: Hachette UK

ISBN: 140130446X

Category: Science

Page: 352

View: 9718

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At the heart of the universe is a steady, insistent beat, the sound of cycles in sync. Along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison; the moon spins in perfect resonance with its orbit around the earth; our hearts depend on the synchronous firing of ten thousand pacemaker cells. While the forces that synchronize the flashing of fireflies may seem to have nothing to do with our heart cells, there is in fact a deep connection. Synchrony is a science in its infancy, and Strogatz is a pioneer in this new frontier in which mathematicians and physicists attempt to pinpoint just how spontaneous order emerges from chaos. From underground caves in Texas where a French scientist spent six months alone tracking his sleep-wake cycle, to the home of a Dutch physicist who in 1665 discovered two of his pendulum clocks swinging in perfect time, this fascinating book spans disciplines, continents, and centuries. Engagingly written for readers of books such as Chaos and The Elegant Universe, Sync is a tour-de-force of nonfiction writing.

An Experimental Approach to Nonlinear Dynamics and Chaos

Author: Nicholas Tufillaro,Tyler Abbott

Publisher: Addison Wesley Publishing Company

ISBN: N.A

Category: Chaotic behavior in systems.

Page: 420

View: 1988

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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.

Chaos in Dynamical Systems

Author: Edward Ott

Publisher: Cambridge University Press

ISBN: 9780521010849

Category: Mathematics

Page: 478

View: 973

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New edition of the best-selling graduate textbook on chaos for scientists and engineers.

Nonlinear Dynamics and Chaos in Agricultural Systems

Author: K. Sakai

Publisher: Gulf Professional Publishing

ISBN: 9780444506467

Category: Mathematics

Page: 204

View: 8774

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An introduction to the analysis of chaos for readers majoring in agricultural science and an introduction to agricultural science for readers majoring in mathematical science and other fields. Hopes some readers will pursue further studies on the chaos of arable land. (Pref.)

Stability, Instability and Chaos

An Introduction to the Theory of Nonlinear Differential Equations

Author: Paul Glendinning

Publisher: Cambridge University Press

ISBN: 9780521425667

Category: Mathematics

Page: 388

View: 1341

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An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.

Nonlinear Dynamics in Circuits

Author: Thomas L. Carroll,Louis M. Pecora

Publisher: World Scientific

ISBN: 9789810224387

Category: Science

Page: 336

View: 4173

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This volume describes the use of simple analog circuits to study nonlinear dynamics, chaos and stochastic resonance. The circuit experiments that are described are mostly easy and inexpensive to reproduce, and yet these experiments come from the forefront of nonlinear dynamics research. The individual chapters describe why analog circuits are so useful for studying nonlinear dynamics, and include theoretical as well as experimental results from some of the leading researchers in the field. Most of the articles contain some tutorial sections for the less experienced readers.The audience for this book includes researchers in nonlinear dynamics, chaos and statistical physics as well as electrical engineering, and graduate and advanced undergraduate students in these fields.

An Introduction to Dynamical Systems and Chaos

Author: G.C. Layek

Publisher: Springer

ISBN: 8132225562

Category: Mathematics

Page: 622

View: 2627

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The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Author: Morris W. Hirsch,Stephen Smale,Robert L. Devaney

Publisher: Academic Press

ISBN: 0123820103

Category: Mathematics

Page: 418

View: 6431

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Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems. Classic text by three of the world's most prominent mathematicians Continues the tradition of expository excellence Contains updated material and expanded applications for use in applied studies