Perspectives of Nonlinear Dynamics: Volume 1
Perspectives of Nonlinear Dynamics: Volume 1

Author: E. Atlee Jackson

Publisher: CUP Archive

Published: 1989

Total Pages: 532

ISBN-13: 9780521426329

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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.

Nonlinear Dynamics, Volume 2
Nonlinear Dynamics, Volume 2

Author: Gaetan Kerschen

Publisher: Springer Science & Business Media

Published: 2014-03-28

Total Pages: 314

ISBN-13: 3319045229

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This second volume of eight from the IMAC - XXXII 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: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data

Nonlinear Dynamics and Chaos: Advances and Perspectives
Nonlinear Dynamics and Chaos: Advances and Perspectives

Author: Marco Thiel

Publisher: Springer

Published: 2010-05-17

Total Pages: 300

ISBN-13: 3642046290

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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.

Understanding Nonlinear Dynamics
Understanding Nonlinear Dynamics

Author: Daniel Kaplan

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 438

ISBN-13: 1461208238

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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.

Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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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.

Introduction to Applied Nonlinear Dynamical Systems and Chaos
Introduction to Applied Nonlinear Dynamical Systems and Chaos

Author: Stephen Wiggins

Publisher: Springer Science & Business Media

Published: 2006-04-18

Total Pages: 860

ISBN-13: 0387217495

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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 Dynamics
Nonlinear Dynamics

Author: Muthusamy Lakshmanan

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 628

ISBN-13: 3642556884

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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.

Nonlinear Dynamics
Nonlinear Dynamics

Author: Marc R Roussel

Publisher: Morgan & Claypool Publishers

Published: 2019-05-01

Total Pages: 190

ISBN-13: 1643274643

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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.

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Author: John Guckenheimer

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 475

ISBN-13: 1461211409

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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.

Nonlinear Dynamics
Nonlinear Dynamics

Author: H.G Solari

Publisher: Routledge

Published: 2019-01-22

Total Pages: 369

ISBN-13: 1351428306

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Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and work