Perspectives Of Nonlinear Dynamics Volume 1

Author : E. Atlee Jackson
Publisher : CUP Archive
Page : 532 pages
File Size : 52,9 Mb
Release : 1989
Category : Mathematics
ISBN : 0521426324

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Perspectives of Nonlinear Dynamics: Volume 1 by E. Atlee Jackson Pdf

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.

Author : E. Atlee Jackson
Publisher : CUP Archive
Page : 676 pages
File Size : 51,8 Mb
Release : 1989
Category : Mathematics
ISBN : 0521426332

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Perspectives of Nonlinear Dynamics: Volume 2 by E. Atlee Jackson Pdf

The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.

Author : Marco Thiel,Jürgen Kurths,M. Carmen Romano,György Károlyi,Alessandro Moura
Publisher : Springer
Page : 293 pages
File Size : 53,6 Mb
Release : 2010-05-17
Category : Science
ISBN : 9783642046292

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Nonlinear Dynamics and Chaos: Advances and Perspectives by Marco Thiel,Jürgen Kurths,M. Carmen Romano,György Károlyi,Alessandro Moura Pdf

This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.

Author : E. Atlee Jackson
Publisher : Unknown
Page : 496 pages
File Size : 51,7 Mb
Release : 1991
Category : Electronic
ISBN : OCLC:1088844980

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Perspectives of Nonlinear Dynamics. Volume I by E. Atlee Jackson Pdf

Author : Edwin Atlee Jackson
Publisher : Unknown
Page : 633 pages
File Size : 55,7 Mb
Release : 1991
Category : Chaotic behavior in systems
ISBN : OCLC:726823780

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Perspectives of Nonlinear Dynamics by Edwin Atlee Jackson Pdf

Author : Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642556883

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Nonlinear Dynamics by Muthusamy Lakshmanan,Shanmuganathan Rajaseekar Pdf

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Author : E. Atlee Jackson
Publisher : Cambridge University Press
Page : 520 pages
File Size : 45,7 Mb
Release : 1992-01-31
Category : Mathematics
ISBN : 0521426324

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Perspectives of Nonlinear Dynamics: Volume 1 by E. Atlee Jackson Pdf

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.

Author : Edwin Atlee Jackson
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 1989
Category : Electronic
ISBN : OCLC:630758117

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Perspectives of Nonlinear Dynamics by Edwin Atlee Jackson Pdf

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 47,5 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

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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 : Edwin Atlee Jackson
Publisher : Unknown
Page : 128 pages
File Size : 53,9 Mb
Release : 1991
Category : Chaotic behavior in systems
ISBN : OCLC:25703323

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Perspectives of Nonlinear Dynamics by Edwin Atlee Jackson Pdf

Author : Leon O Chua
Publisher : World Scientific
Page : 360 pages
File Size : 52,8 Mb
Release : 2009-08-11
Category : Computers
ISBN : 9789814468947

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Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A - Volume Iii by Leon O Chua Pdf

Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli στ-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and hyper Bernoulli wave dynamics. Explicit global state transition formulas derived for rules 60, 90, 105, and 150 reveal a new scale-free phenomenon. The most surprising new result unveiled in this volume is the “Isle of Eden” found hidden in most (almost 90%) of the 256 local rules. Readers are challenged to hunt for long-period, isolated Isles of Eden. These are rare gems waiting to be discovered.

Author : Gaetan Kerschen,Douglas Adams,Alex Carrella
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 46,9 Mb
Release : 2013-05-24
Category : Technology & Engineering
ISBN : 9781461465706

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Topics in Nonlinear Dynamics, Volume 1 by Gaetan Kerschen,Douglas Adams,Alex Carrella Pdf

Topics in Nonlinear Dynamics, Volume 1: Proceedings of the 31st IMAC, A Conference and Exposition on Structural Dynamics, 2013, the first volume of seven from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Nonlinear Oscillations Nonlinearities ... In Practice Nonlinear System Identification: Methods Nonlinear System Identification: Friction & Contact Nonlinear Modal Analysis Nonlinear Modeling & Simulation Nonlinear Vibration Absorbers Constructive Utilization of Nonlinearity

Author : Dimitri Volchenkov,Albert C. J. Luo
Publisher : Springer Nature
Page : 198 pages
File Size : 51,6 Mb
Release : 2022-07-29
Category : Technology & Engineering
ISBN : 9783030973285

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New Perspectives on Nonlinear Dynamics and Complexity by Dimitri Volchenkov,Albert C. J. Luo Pdf

This book presents select, recent developments in nonlinear and complex systems reported at the 1st Online Conference on Nonlinear Dynamics and Complexity, held on November 23-25, 2020. It provides an exchange recent developments, discoveries, and progresses in Nonlinear Dynamics and Complexity. The collection presents fundamental and frontier theories and techniques for modern science and technology, stimulates more research interest for exploration of nonlinear science and complexity; and passes along new knowledge and insight to the next generation of engineers and technologists in a range of fields.

Author : Steven H Strogatz
Publisher : CRC Press
Page : 616 pages
File Size : 49,7 Mb
Release : 2024-01-16
Category : Mathematics
ISBN : 9780429676284

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Nonlinear Dynamics and Chaos by Steven H Strogatz Pdf

The goal of this third edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering is the same as previous editions: to provide a good foundation - and a joyful experience - for anyone who’d like to learn about nonlinear dynamics and chaos from an applied perspective. 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 prerequisites are comfort with multivariable calculus and linear algebra, as well as a first course in physics. Ideas from probability, complex analysis, and Fourier analysis are invoked, but they're either worked out from scratch or can be safely skipped (or accepted on faith). Changes to this edition include substantial exercises about conceptual models of climate change, an updated treatment of the SIR model of epidemics, and amendments (based on recent research) about the Selkov model of oscillatory glycolysis. Equations, diagrams, and every word has been reconsidered and often revised. There are also about 50 new references, many of them from the recent literature. The most notable change is a new chapter. Chapter 13 is about the Kuramoto model. The Kuramoto model is an icon of nonlinear dynamics. Introduced in 1975 by the Japanese physicist Yoshiki Kuramoto, his elegant model is one of the rare examples of a high-dimensional nonlinear system that can be solved by elementary means. Students and teachers have embraced the book in the past, its general approach and framework continue to be sound.

Author : Bhimsen K. Shivamoggi
Publisher : Springer
Page : 375 pages
File Size : 48,6 Mb
Release : 2014-05-14
Category : Technology & Engineering
ISBN : 9789400770942

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Nonlinear Dynamics and Chaotic Phenomena: An Introduction by Bhimsen K. Shivamoggi Pdf

This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special emphasis on some aspects of fluid dynamics and plasma physics reflecting the author’s involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on. This book has grown out of the author’s lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum. This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering. This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises.