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| nonlinear dynamical systems and chaos strogatz: Nonlinear Dynamics and Chaos Steven H. Strogatz, 2018-05-04 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. |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Dynamics and Chaos with Student Solutions Manual Steven H. Strogatz, 2018-09-21 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. |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Dynamics and Chaos J. M. T. Thompson, H. B. Stewart, 2002-02-15 Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area 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 since first edition Glossary of terms and a bibliography have been added All figures and illustrations will be 'modernised' Comprehensive and systematic account of nonlinear dynamics and chaos, still a fast-growing area of applied mathematics Highly illustrated Excellent introductory text, can be used for an advanced undergraduate/graduate course text |
| nonlinear dynamical systems and chaos strogatz: Introduction to Applied Nonlinear Dynamical Systems and Chaos Stephen Wiggins, 2003-10-01 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 |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Dynamics and Chaos STEVEN H. STROGATZ, Taylor & Francis Group, 2019-07-10 |
| nonlinear dynamical systems and chaos strogatz: Chaos in Dynamical Systems Edward Ott, 2002-08-22 Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject. |
| nonlinear dynamical systems and chaos strogatz: An Introduction To Chaotic Dynamical Systems Robert Devaney, 2018-03-09 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. |
| nonlinear dynamical systems and chaos strogatz: An Introduction to Symbolic Dynamics and Coding Douglas Lind, Brian Marcus, 2021-01-21 Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C^*$-algebras. This Second Edition maintains the introductory character of the original 1995 edition as a general textbook on symbolic dynamics and its applications to coding. It is written at an elementary level and aimed at students, well-established researchers, and experts in mathematics, electrical engineering, and computer science. Topics are carefully developed and motivated with many illustrative examples. There are more than 500 exercises to test the reader's understanding. In addition to a chapter in the First Edition on advanced topics and a comprehensive bibliography, the Second Edition includes a detailed Addendum, with companion bibliography, describing major developments and new research directions since publication of the First Edition. |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Dynamics in Complex Systems Armin Fuchs, 2012-09-23 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) |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Ordinary Differential Equations Dominic Jordan, Peter Smith, 2007-08-23 This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinicbifurcation and Liapunov exponents.Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007).Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences. |
| nonlinear dynamical systems and chaos strogatz: Differential Equations and Dynamical Systems Lawrence Perko, 2012-12-06 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. |
| nonlinear dynamical systems and chaos strogatz: Chaos and Nonlinear Dynamics Robert C. Hilborn, 1994 Mathematics of Computing -- Miscellaneous. |
| nonlinear dynamical systems and chaos strogatz: Differential Dynamical Systems James D. Meiss, 2007-01-01 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 conceptsflow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. 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. Audience This textbook is intended for senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with elementary differential equations and linear algebra and should have had exposure to advanced calculus. Contents List of Figures; Preface; Acknowledgments; Chapter 1: Introduction; Chapter 2: Linear Systems; Chapter 3: Existence and Uniqueness; Chapter 4: Dynamical Systems; Chapter 5: Invariant Manifolds; Chapter 6: The Phase Plane; Chapter 7: Chaotic Dynamics; Chapter 8: Bifurcation Theory; Chapter 9: Hamiltonian Dynamics; Appendix: Mathematical Software; Bibliography; Index |
| nonlinear dynamical systems and chaos strogatz: Ordinary Differential Equations Morris Tenenbaum, Harry Pollard, 1985-10-01 Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more. |
| nonlinear dynamical systems and chaos strogatz: Synchronization in Complex Networks of Nonlinear Dynamical Systems Chai Wah Wu, 2007 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. |
| nonlinear dynamical systems and chaos strogatz: Number Theory and Dynamical Systems M. M. Dodson, 1989-11-09 This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems. |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields John Guckenheimer, Philip Holmes, 2014-09-01 |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Ordinary Differential Equations R. Grimshaw, 2017-10-19 Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations. |
| nonlinear dynamical systems and chaos strogatz: An Introduction to Dynamical Systems D. K. Arrowsmith, C. M. Place, 1990-07-27 In recent years there has been an explosion of research centred on the appearance of so-called 'chaotic behaviour'. This book provides a largely self contained introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit this sort of behaviour. The early part of this book is based on lectures given at the University of London and covers the background to dynamical systems, the fundamental properties of such systems, the local bifurcation theory of flows and diffeomorphisms, Anosov automorphism, the horseshoe diffeomorphism and the logistic map and area preserving planar maps . The authors then go on to consider current research in this field such as the perturbation of area-preserving maps of the plane and the cylinder. This book, which has a great number of worked examples and exercises, many with hints, and over 200 figures, will be a valuable first textbook to both senior undergraduates and postgraduate students in mathematics, physics, engineering, and other areas in which the notions of qualitative dynamics are employed. |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Dynamics George Datseris, Ulrich Parlitz, 2022-03-14 This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills. |
| nonlinear dynamical systems and chaos strogatz: The Joy of X Steven Henry Strogatz, 2012 A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the New York Times. |
| nonlinear dynamical systems and chaos strogatz: Complex Systems Science in Biomedicine Thomas Deisboeck, J. Yasha Kresh, 2007-06-13 Complex Systems Science in Biomedicine Thomas S. Deisboeck and J. Yasha Kresh Complex Systems Science in Biomedicine covers the emerging field of systems science involving the application of physics, mathematics, engineering and computational methods and techniques to the study of biomedicine including nonlinear dynamics at the molecular, cellular, multi-cellular tissue, and organismic level. With all chapters helmed by leading scientists in the field, Complex Systems Science in Biomedicine's goal is to offer its audience a timely compendium of the ongoing research directed to the understanding of biological processes as whole systems instead of as isolated component parts. In Parts I & II, Complex Systems Science in Biomedicine provides a general systems thinking perspective and presents some of the fundamental theoretical underpinnings of this rapidly emerging field. Part III then follows with a multi-scaled approach, spanning from the molecular to macroscopic level, exemplified by studying such diverse areas as molecular networks and developmental processes, the immune and nervous systems, the heart, cancer and multi-organ failure. The volume concludes with Part IV that addresses methods and techniques driven in design and development by this new understanding of biomedical science. Key Topics Include: • Historic Perspectives of General Systems Thinking • Fundamental Methods and Techniques for Studying Complex Dynamical Systems • Applications from Molecular Networks to Disease Processes • Enabling Technologies for Exploration of Systems in the Life Sciences Complex Systems Science in Biomedicine is essential reading for experimental, theoretical, and interdisciplinary scientists working in the biomedical research field interested in a comprehensive overview of this rapidly emerging field. About the Editors: Thomas S. Deisboeck is currently Assistant Professor of Radiology at Massachusetts General Hospital and Harvard Medical School in Boston. An expert in interdisciplinary cancer modeling, Dr. Deisboeck is Director of the Complex Biosystems Modeling Laboratory which is part of the Harvard-MIT Martinos Center for Biomedical Imaging. J. Yasha Kresh is currently Professor of Cardiothoracic Surgery and Research Director, Professor of Medicine and Director of Cardiovascular Biophysics at the Drexel University College of Medicine. An expert in dynamical systems, he holds appointments in the School of Biomedical Engineering and Health Systems, Dept. of Mechanical Engineering and Molecular Pathobiology Program. Prof. Kresh is Fellow of the American College of Cardiology, American Heart Association, Biomedical Engineering Society, American Institute for Medical and Biological Engineering. |
| nonlinear dynamical systems and chaos strogatz: Instabilities, Chaos and Turbulence Paul Manneville, 2010 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. |
| nonlinear dynamical systems and chaos strogatz: Differential Equations, Dynamical Systems, and an Introduction to Chaos Morris W. Hirsch, Stephen Smale, Robert L. Devaney, 2003-12-06 Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition, provides a rigorous yet accessible introduction to differential equations and dynamical systems. The original text by three of the world's leading mathematicians has become the standard textbook for graduate courses in this area. Thirty years in the making, this Second Edition brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems. This book will be particularly useful to advanced students and practitioners in higher mathematics. - Developed by award-winning researchers and authors - Provides a rigorous yet accessible introduction to differential equations and dynamical systems - Includes bifurcation theory throughout - Contains numerous explorations for students to embark upon NEW IN THIS EDITION - New contemporary material and updated applications - Revisions throughout the text, including simplification of many theorem hypotheses - Many new figures and illustrations - Simplified treatment of linear algebra - Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor - Increased coverage of discrete dynamical systems |
| nonlinear dynamical systems and chaos strogatz: Chaos Kathleen T. Alligood, Tim D. Sauer, James A. Yorke, 2006-04-06 Developed and class-tested by a distinguished team of authors at two universities, this text is intended for courses in nonlinear dynamics in either mathematics or physics. The only prerequisites are calculus, differential equations, and linear algebra. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits -- short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed for use with any software package. And each chapter ends with a Challenge, guiding students through an advanced topic in the form of an extended exercise. |
| nonlinear dynamical systems and chaos strogatz: Hyperbolic Chaos Sergey P. Kuznetsov, 2012-03-20 Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia. |
| nonlinear dynamical systems and chaos strogatz: Dynamics and Bifurcations Jack K. Hale, Hüseyin Kocak, 1996-12-01 In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears. |
| nonlinear dynamical systems and chaos strogatz: The Calculus of Friendship Steven Strogatz, 2011-03-07 The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey. |
| nonlinear dynamical systems and chaos strogatz: Elements of Applied Bifurcation Theory Yuri Kuznetsov, 2004-06-29 Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis. |
| nonlinear dynamical systems and chaos strogatz: Backstepping Control of Nonlinear Dynamical Systems Sundarapandian Vaidyanathan, Ahmad Taher Azar, 2020-08-15 Backstepping Control of Nonlinear Dynamical Systems addresses both the fundamentals of backstepping control and advances in the field. The latest techniques explored include 'active backstepping control', 'adaptive backstepping control', 'fuzzy backstepping control' and 'adaptive fuzzy backstepping control'. The reference book provides numerous simulations using MATLAB and circuit design. These illustrate the main results of theory and applications of backstepping control of nonlinear control systems. Backstepping control encompasses varied aspects of mechanical engineering and has many different applications within the field. For example, the book covers aspects related to robot manipulators, aircraft flight control systems, power systems, mechanical systems, biological systems and chaotic systems. This multifaceted view of subject areas means that this useful reference resource will be ideal for a large cross section of the mechanical engineering community. - Details the real-world applications of backstepping control - Gives an up-to-date insight into the theory, uses and application of backstepping control - Bridges the gaps for different fields of engineering, including mechanical engineering, aeronautical engineering, electrical engineering, communications engineering, robotics and biomedical instrumentation |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Waves, Solitons and Chaos Eryk Infeld, George Rowlands, 2000-07-13 This revised and updated second edition of a highly successful book is the only text at this level to embrace a universal approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos. The authors now include new material on biology and laser theory, and go on to discuss important recent developments such as soliton metamorphosis. A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Each chapter concludes with a set of problems. This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general, it will be of value to final year undergraduates and beginning graduate students studying fluid dynamics, plasma physics and applied mathematics. |
| nonlinear dynamical systems and chaos strogatz: The Illustrated Dictionary of Nonlinear Dynamics and Chaos Tomasz Kapitaniak, Steven R. Bishop, 1999-03-03 The study of nonlinear dynamics is one of the most active fields in modern science. It reaches across the whole range of scientific study, and is applied in fields as diverse as physics, engineering, biology, economics and medicine. However, the mathematical language used to describe nonlinear dynamics, and the proliferation of new terminology, can make the use of nonlinear dynamics a daunting task to the non-specialist. In addition,the simultaneous growth in the use of nonlinear dynamics across different fields, and the cross-fertilization of ideas from different disciplines, mean that names and methods used and developed in one field may be altered when 're-discovered' in a different context, making understanding the literature a difficult and time-consuming task. The Illustrated Dictionary of Nonlinear Dynamics and Chaos addresses these problems. It presents, in an alphabetical format, the key terms, theorems and equations which arise in the study of nonlinear dynamics. New mathematical ideas are described and explained with examples and, where appropriate, illustrations are included to aid clarification and understanding. For some entries, the descriptions are self-contained, but should more detail be required, references are included for further reading. Where alternative terms are used for a single concept, an entry is placed under the name in most common usage, with cross-references given under other names. The Illustrated Dictionary of Nonlinear Dynamics and Chaos is an invaluable reference source for all those who use nonlinear dynamics in their research, whether they are newcomers to the field who need help to understand the literature, or more experienced researchers who need a concise and handy reference. |
| nonlinear dynamical systems and chaos strogatz: Calculus Made Easy Silvanus P. Thompson, Martin Gardner, 2014-03-18 Calculus Made Easy by Silvanus P. Thompson and Martin Gardner has long been the most popular calculus primer. This major revision of the classic math text makes the subject at hand still more comprehensible to readers of all levels. With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader. |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Electrodynamics in Biological Systems W. Adey, 2012-12-06 The past half century has seen an extraordinary growth in the fields of cellular and molecular biology. From simple morphologi cal concepts of cells as the essential units of living matter there has been an ever-sharper focus on functional organization of living systems, with emphasis on molecular dynamics. Thus, life forms have come to be defined increasingly in terms of metabolism, growth, reproduction and responses to environmental perturbations. Since these properties occur in varying degrees in systems below the level of cellular organization, there has been a blurring of older models that restricted the concepts of life to cellular systems. At the same time, a search has begun for elemental as pects of molecular and atomic behavior that might better define properties common to all life forms. This search has led to an examination of nonlinear behavior in biological macromolecules, whether in response to electrical or chemical stimulation, for example, or as a means of signaling along a molecular chain, or as a means of energy transfer. Experimental knowledge in this area has grown rapidly in the past decade, and in some respects has outstripped theoretical models adequate to ex plain these new observations. Nevertheless, it can be claimed that there is now an impressive body of experiments implicating non linear, nonequilibrium processes as fundamental steps in sequential operations of biological systems. |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Dynamics and Chaos Steven Henry Strogatz, 2000 |
| nonlinear dynamical systems and chaos strogatz: Introduction to Dynamics Ian Percival, Derek Richards, 1982-12-02 In this book, the subject of dynamics is introduced at undergraduate level through the elementary qualitative theory of differential equations, the geometry of phase curves and the theory of stability. The text is supplemented with over a hundred exercises. |
| nonlinear dynamical systems and chaos strogatz: Infinite Powers Steven Strogatz, 2019 This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Aristotle to today's million-dollar reward that awaits whoever cracks Reimann's hypothesis. Filled with idiosyncratic characters from Pythagoras to Euler, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilization, including science, politics, ethics, philosophy, and much besides. |
| nonlinear dynamical systems and chaos strogatz: An Introduction to Dynamical Systems Rex Clark Robinson, 2012 This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course. The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally, chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems. The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets. In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book. This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations. |
| nonlinear dynamical systems and chaos strogatz: Nonlinear Dynamics and Chaos, 2nd ed. SET with Student Solutions Manual Steven H. Strogatz, 2016-08-23 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. |
Home | Nonlinear Dynamics - Springer
Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The journal covers nonlinear dynamics …
Methods in Nonlinear Analysis - SpringerLink
Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials …
Nonlinear Acoustics - SpringerLink
Chapters 10 through 15 cover applications and additional methodologies encountered in nonlinear acoustics that include perturbation and numerical methods, ray theory for inhomogeneous …
Home | Journal of Nonlinear Science - Springer
The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. It features papers …
Nonlinear Systems: Analysis, Stability, and Control | SpringerLink
Coupled with this set of analytic advances has been the vast increase in computational power available for both the simulation and visualization of nonlinear systems as well as for the …
Articles | Nonlinear Dynamics - Springer
4 days ago · Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The ...
Nonlinear Dynamics: A Concise Introduction Interlaced with Code ...
This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at …
Data-driven nonlinear and stochastic dynamics with control
Dec 16, 2024 · The analysis is developed with reference to a nonlinear beam where the two boundary conditions have nonlinearities and masses, with the goal of identifying the uncertain …
Lectures on Nonlinear Dynamics - SpringerLink
This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, …
Aims and scope | Nonlinear Dynamics - Springer
Nonlinear Dynamics provides a forum for the rapid publication of original research in the field of nonlinear dynamics. The scope of the journal encompasses all nonlinear dynamic phenomena …
Home | Nonlinear Dynamics - Springer
Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The journal covers nonlinear dynamics …
Methods in Nonlinear Analysis - SpringerLink
Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials …
Nonlinear Acoustics - SpringerLink
Chapters 10 through 15 cover applications and additional methodologies encountered in nonlinear acoustics that include perturbation and numerical methods, ray theory for inhomogeneous …
Home | Journal of Nonlinear Science - Springer
The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. It features papers …
Nonlinear Systems: Analysis, Stability, and Control | SpringerLink
Coupled with this set of analytic advances has been the vast increase in computational power available for both the simulation and visualization of nonlinear systems as well as for the …
Articles | Nonlinear Dynamics - Springer
4 days ago · Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The ...
Nonlinear Dynamics: A Concise Introduction Interlaced with Code ...
This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at …
Data-driven nonlinear and stochastic dynamics with control
Dec 16, 2024 · The analysis is developed with reference to a nonlinear beam where the two boundary conditions have nonlinearities and masses, with the goal of identifying the uncertain …
Lectures on Nonlinear Dynamics - SpringerLink
This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, …
Aims and scope | Nonlinear Dynamics - Springer
Nonlinear Dynamics provides a forum for the rapid publication of original research in the field of nonlinear dynamics. The scope of the journal encompasses all nonlinear dynamic phenomena …
