Introduction To Applied Nonlinear Dynamical Systems And Chaos

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 844 pages
File Size : 50,9 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387217499

Get Book

Introduction to Applied Nonlinear Dynamical Systems and Chaos by Stephen Wiggins Pdf

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

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 860 pages
File Size : 44,5 Mb
Release : 2003-10-01
Category : Mathematics
ISBN : 9780387001777

Get Book

Introduction to Applied Nonlinear Dynamical Systems and Chaos by Stephen Wiggins Pdf

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

Author : Stephen Wiggins
Publisher : Unknown
Page : 688 pages
File Size : 40,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475740689

Get Book

Introduction to Applied Nonlinear Dynamical Systems and Chaos by Stephen Wiggins Pdf

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 49,6 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

Get Book

Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

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 : Marian Wiercigroch,Bram de Kraker
Publisher : World Scientific
Page : 466 pages
File Size : 45,7 Mb
Release : 2000
Category : Technology & Engineering
ISBN : 9810229275

Get Book

Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities by Marian Wiercigroch,Bram de Kraker Pdf

Annotation Consisting primarily of contributions written by engineers from Europe, Asia, and the US, this volume provides a general methodology for describing, solving, and analyzing discontinuous systems. The focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction, or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials, and dynamics of metal cutting. Of likely interest to new and experienced researchers working in the field of applied mathematics and physics, mechanical and civil engineering, and manufacturing. Lacks a subject index. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Ali H. Nayfeh,Balakumar Balachandran
Publisher : John Wiley & Sons
Page : 700 pages
File Size : 54,5 Mb
Release : 2008-11-20
Category : Science
ISBN : 9783527617555

Get Book

Applied Nonlinear Dynamics by Ali H. Nayfeh,Balakumar Balachandran Pdf

A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.

Author : Jan A. Sanders,Ferdinand Verhulst
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 42,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475745757

Get Book

Averaging Methods in Nonlinear Dynamical Systems by Jan A. Sanders,Ferdinand Verhulst Pdf

In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.

Author : Andrew Fowler,Mark McGuinness
Publisher : Springer Nature
Page : 303 pages
File Size : 44,8 Mb
Release : 2020-02-06
Category : Mathematics
ISBN : 9783030325381

Get Book

Chaos by Andrew Fowler,Mark McGuinness Pdf

This is a textbook on chaos and nonlinear dynamics, written by applied mathematicians for applied mathematicians. It aims to tread a middle ground between the mathematician's rigour and the physicist’s pragmatism. While the subject matter is now classical and can be found in many other books, what distinguishes this book is its philosophical approach, its breadth, its conciseness, and its exploration of intellectual byways, as well as its liberal and informative use of illustration. Written at the graduate student level, the book occasionally drifts from classical material to explore new avenues of thought, sometimes in the exercises. A key feature of the book is its holistic approach, encompassing the development of the subject since the time of Poincaré, and including detailed material on maps, homoclinic bifurcations, Hamiltonian systems, as well as more eclectic items such as Julia and Mandelbrot sets. Some of the more involved codes to produce the figures are described in the appendix. Based on lectures to upper undergraduates and beginning graduate students, this textbook is ideally suited for courses at this level and each chapter includes a set of exercises of varying levels of difficulty.

Author : Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Publisher : Academic Press
Page : 433 pages
File Size : 40,9 Mb
Release : 2004
Category : Business & Economics
ISBN : 9780123497031

Get Book

Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris W. Hirsch,Stephen Smale,Robert L. Devaney Pdf

Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.

Author : James D. Meiss
Publisher : SIAM
Page : 392 pages
File Size : 42,6 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9781611974645

Get Book

Differential Dynamical Systems, Revised Edition by James D. Meiss Pdf

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

Author : Paul Manneville
Publisher : World Scientific
Page : 456 pages
File Size : 46,7 Mb
Release : 2010
Category : Science
ISBN : 9781848163928

Get Book

Instabilities, Chaos and Turbulence by Paul Manneville Pdf

This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.

Author : John Guckenheimer,Philip Holmes
Publisher : Springer Science & Business Media
Page : 475 pages
File Size : 51,9 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781461211402

Get Book

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by John Guckenheimer,Philip Holmes Pdf

An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Author : Robert Devaney
Publisher : CRC Press
Page : 251 pages
File Size : 41,7 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9780429981937

Get Book

An Introduction To Chaotic Dynamical Systems by Robert Devaney Pdf

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.

Author : Santo Banerjee,Mala Mitra,Lamberto Rondoni
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 48,7 Mb
Release : 2011-09-10
Category : Technology & Engineering
ISBN : 9783642219214

Get Book

Applications of Chaos and Nonlinear Dynamics in Engineering - by Santo Banerjee,Mala Mitra,Lamberto Rondoni Pdf

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications

Author : Lawrence Perko
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402490

Get Book

Differential Equations and Dynamical Systems by Lawrence Perko Pdf

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 bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer 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 Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.