Nonlinear Dynamical Systems: 1983-1995 PDF Download

Author: Jan Awrejcewicz
Publisher:
ISBN:
Category : Chaotic behavior in systems
Languages : en
Pages : 1138

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Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532

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Book Description
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: Ferdinand Verhulst
Publisher: Springer Science & Business Media
ISBN: 3642971490
Category : Mathematics
Languages : en
Pages : 287

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Book Description
Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.

Author: Marc R Roussel
Publisher: Morgan & Claypool Publishers
ISBN: 1643274643
Category : Science
Languages : en
Pages : 190

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Book Description
This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. This book also provides a survey that can be taught in a single academic term covering a greater variety of dynamical systems (discrete versus continuous time, finite versus infinite-dimensional, dissipative versus conservative) than is normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented.

Author: Lawrence Perko
Publisher: Springer Science & Business Media
ISBN: 1468402498
Category : Mathematics
Languages : en
Pages : 530

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Book Description
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.

Author: Robert Devaney
Publisher: CRC Press
ISBN: 0429981937
Category : Mathematics
Languages : en
Pages : 280

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Book Description
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: Wassim M. Haddad
Publisher: Princeton University Press
ISBN: 1400841046
Category : Mathematics
Languages : en
Pages : 975

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Book Description
Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.

Author: Stephen Wiggins
Publisher: Springer Science & Business Media
ISBN: 0387217495
Category : Mathematics
Languages : en
Pages : 860

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Book Description
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: Richard A. Heath
Publisher: Psychology Press
ISBN: 1135670552
Category : Psychology
Languages : en
Pages : 400

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Book Description
Additional Resource Materials Human behavior would not be interesting to us if it remained the same from one moment to the next. Moreover, we tend to be sensitive to changes in people's behavior, especially when such change impacts on our own, and other's, behavior. This book describes a variety of techniques for investigating change in behavior. It employs conventional time series methods, as well as recently developed methodology using nonlinear dynamics, including chaos, a term that is not easy to define, nor to confirm. Although nonlinear methods are being used more frequently in psychology, a comprehensive coverage of methods, theory and applications, with a particular focus on human behavior, is needed. Between these covers, the reader is led through various procedures for linear and nonlinear time series analysis, including some novel procedures that allow subtle temporal aspects of human cognition to be detected. Analyses of reaction times, heart-rate, psychomotor skill, decision making, and EEG are supplemented by a contemporary review of recent dynamical research in developmental psychology, psychopathology, and human cognitive processes. A consideration of nonlinear dynamics assists our understanding of deep issues such as: Why is our short-term memory capacity limited? Why do chronic disorders, and also cognitive development, progress through stage-like transitions? Why do people make irrational decisions? This book will be of particular interest to researchers, practitioners, and advanced students in a variety of areas in psychology, particularly in human experimental and physiological psychology. Data analyses are performed using the latest nonlinear dynamics computer packages. A comprehensive WWW resource of software and supplementary information is provided to assist the reader's understanding of the novel, and potentially revolutionary, procedures described in the book.

Author: Henk Broer
Publisher: Springer Science & Business Media
ISBN: 1441968709
Category : Mathematics
Languages : en
Pages : 313

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Book Description
Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.