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| Author | : Stephen Wiggins |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 860 |
| Release | : 2006-04-18 |
| Genre | : Mathematics |
| ISBN | : 0387217495 |
Download Introduction to Applied Nonlinear Dynamical Systems and Chaos Book in PDF, ePub and Kindle
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 | : Steven H. Strogatz |
| Publisher | : CRC Press |
| Total Pages | : 532 |
| Release | : 2018-05-04 |
| Genre | : Mathematics |
| ISBN | : 0429961111 |
Download Nonlinear Dynamics and Chaos Book in PDF, ePub and Kindle
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 | : Ali H. Nayfeh |
| Publisher | : John Wiley & Sons |
| Total Pages | : 700 |
| Release | : 2008-11-20 |
| Genre | : Science |
| ISBN | : 3527617558 |
Download Applied Nonlinear Dynamics Book in PDF, ePub and Kindle
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 | : Marian Wiercigroch |
| Publisher | : World Scientific |
| Total Pages | : 466 |
| Release | : 2000 |
| Genre | : Technology & Engineering |
| ISBN | : 9789810229276 |
Download Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities Book in PDF, ePub and Kindle
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 | : Jan A. Sanders |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 259 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475745753 |
Download Averaging Methods in Nonlinear Dynamical Systems Book in PDF, ePub and Kindle
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 | : Daniel Kaplan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 438 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461208238 |
Download Understanding Nonlinear Dynamics Book in PDF, ePub and Kindle
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.
| Author | : Robert Devaney |
| Publisher | : CRC Press |
| Total Pages | : 251 |
| Release | : 2018-03-09 |
| Genre | : Mathematics |
| ISBN | : 0429981937 |
Download An Introduction To Chaotic Dynamical Systems Book in PDF, ePub and Kindle
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 | : Andrew Fowler |
| Publisher | : Springer Nature |
| Total Pages | : 303 |
| Release | : 2020-02-06 |
| Genre | : Mathematics |
| ISBN | : 3030325385 |
Download Chaos Book in PDF, ePub and Kindle
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 | : John Guckenheimer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 475 |
| Release | : 2013-11-21 |
| Genre | : Mathematics |
| ISBN | : 1461211409 |
Download Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields Book in PDF, ePub and Kindle
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 | : James D. Meiss |
| Publisher | : SIAM |
| Total Pages | : 392 |
| Release | : 2017-01-24 |
| Genre | : Mathematics |
| ISBN | : 161197464X |
Download Differential Dynamical Systems, Revised Edition Book in PDF, ePub and Kindle
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.
