Lectures On Nonlinear Dynamics
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Lectures On Nonlinear Dynamics
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Author : José Roberto Castilho Piqueira
language : en
Publisher: Springer Nature
Release Date : 2024-01-03
Lectures On Nonlinear Dynamics written by José Roberto Castilho Piqueira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-03 with Technology & Engineering categories.
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, nonlinear modal analysis and model reduction, synchronization, and strongly nonlinear dynamics. Interwoven seamlessly, these groups cover a wide range of topics, from fundamental concepts to practical applications, catering to both introductory and advanced readers. The first group, consisting of chapters 1 and 2, serves as an introduction to the theory of parametric resonance and the dynamics of parametrically excited slender structures. Chapters 3, 4, and 5 form the second group, offering insights into normal forms, nonlinear normal modes, and nonlinear system identification. Chapters 6 and 7 delve into asynchronous modes of structural vibration and master-slave topologies for time signal distribution within synchronous systems, respectively, representing the third group. Finally, the last four chapters tackle the fourth group, exploring nonlinear dynamics of variable mass oscillators, advanced analytical methods for strong nonlinear vibration problems, chaos theory, and dynamic integrity from the perspectives of safety and design. This book harmoniously combines theoretical depth and practical relevance to provide a comprehensive understanding of nonlinear dynamics.
Introduction To Nonlinear Dynamics For Physicists
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Author : H D I Abarbanel
language : en
Publisher: World Scientific
Release Date : 1993-06-23
Introduction To Nonlinear Dynamics For Physicists written by H D I Abarbanel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-23 with Science categories.
This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon. Contents:IntroductionNonlinear Oscillator without DissipationEquilibrium States of a Nonlinear Oscillator with DissipationOscillations in Systems with Nonlinear Dissipation-GeneratorsThe Van der Pol GeneratorThe Poincaré MapSlow and Fast Motions in Systems with One Degree of FreedomForced Nonlinear Oscillators: Linear and Nonlinear ResonancesForced Generator: SynchronizationCompetition of ModesPoincaré Indices and Bifurcations of Equilibrium StatesResonance Interactions between OscillatorsSolitonsSteady Propagation of Shock WavesFormation of Shock WavesSolitons. Shock Waves. Wave Interaction. The Spectral ApproachWeak Turbulence. Random Phase ApproximationRegular Patterns in Dissipative MediaDeterministic Chaos. Qualitative DescriptionDescription of a Circuit with Chaos. Chaos in MapsBifurcations of Periodic Motions. Period DoublingControlled Nonlinear Oscillator. IntermittencyScenarios of the Onset of Chaos. Chaos through Quasi-PeriodicityCharacteristics of Chaos. Experimental Observation of ChaosMultidimensional Chaos. Discrete Ginzburg-Landau ModelProblems to Accompany the Lectures Readership: Physicists. keywords: “These lecture notes briefly introduce the reader to new ideas, so would be a useful addition to a library or a source of ideas for lectures or projects; a good student may also find this text useful as a quick introduction to many new ideas.” Contemporary Physics “Introduction to Nonlinear Dynamics for Physicists … is a compact and fairly terse high-level set of 24 lectures.” New Scientist
Nonlinear Dynamics
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Author : Rowena Ball
language : en
Publisher: World Scientific
Release Date : 2003
Nonlinear Dynamics written by Rowena Ball and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book is an inspirational introduction to modern research directions and scholarship in nonlinear dynamics, and will also be a valuable reference for researchers in the field. With the scholarly level aimed at the beginning graduate student, the book will have broad appeal to those with an undergraduate background in mathematical or physical sciences. In addition to pedagogical and new material, each chapter reviews the current state of the area and discusses classic and open problems in engaging, surprisingly non-technical ways. The contributors are Brian Davies (bifurcations in maps), Nalini Joshi (integrable systems and asymptotics), Alan Newell (wave turbulence and pattern formation), Mark Ablowitz (nonlinear waves), Carl Weiss (spatial solitons), Cathy Holmes (Hamiltonian systems), Tony Roberts (dissipative fluid mechanics), Jorgen Frederiksen (two-dimensional turbulence), and Mike Lieberman (Fermi acceleration).
Lectures On Nonlinear Mechanics And Chaos Theory
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Author : Albert W. Stetz
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016
Lectures On Nonlinear Mechanics And Chaos Theory written by Albert W. Stetz and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Science categories.
Lagrangian dynamics -- Noether's theorem -- Hamiltonian formulation -- Hamilton's principle function -- Hamilton's characteristic function -- Action-angle variables -- Abstract transformation theory -- Poisson brackets -- Liouville's theorem -- Preturbation theory -- The Henon-Heiles oscillator -- Discrete maps -- Lyapunov exponents -- The Poincaré-Birkoff theorem -- The KAM theorem -- Ergodic hypothesis -- Measure theory
Nonlinear Dynamics Materials Theory And Experiments
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Author : Mustapha Tlidi
language : en
Publisher: Springer
Release Date : 2015-11-14
Nonlinear Dynamics Materials Theory And Experiments written by Mustapha Tlidi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-14 with Science categories.
This book presents recent advances, new ideas and novel techniques related to the field of nonlinear dynamics, including localized pattern formation, self-organization and chaos. Various natural systems ranging from nonlinear optics to mechanics, fluids and magnetic are considered. The aim of this book is to gather specialists from these various fields of research to promote cross-fertilization and transfer of knowledge between these active research areas. In particular, nonlinear optics and laser physics constitute an important part in this issue due to the potential applications for all-optical control of light, optical storage, and information processing. Other possible applications include the generation of ultra-short pulses using all-fiber cavities.
Nonlinear Dynamics Chaotic And Complex Systems
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Author : Eryk Infeld
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-19
Nonlinear Dynamics Chaotic And Complex Systems written by Eryk Infeld and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-19 with Mathematics categories.
The physics and mathematics of nonlinear dynamics, chaotic and complex systems constitute some of the most fascinating developments of late twentieth century science. It turns out that chaotic bahaviour can be understood, and even utilized, to a far greater degree than had been suspected. Surprisingly, universal constants have been discovered. The implications have changed our understanding of important phenomena in physics, biology, chemistry, economics, medicine and numerous other fields of human endeavor. In this book, two dozen scientists and mathematicians who were deeply involved in the "nonlinear revolution" cover most of the basic aspects of the field.
International Conference On Theory And Application In Nonlinear Dynamics Icand 2012
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Author : Visarath In
language : en
Publisher: Springer
Release Date : 2013-12-13
International Conference On Theory And Application In Nonlinear Dynamics Icand 2012 written by Visarath In and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-13 with Technology & Engineering categories.
A collection of different lectures presented by experts in the field of nonlinear science provides the reader with contemporary, cutting-edge, research works that bridge the gap between theory and device realizations of nonlinear phenomena. Representative examples of topics covered include: chaos gates, social networks, communication, sensors, lasers, molecular motors, biomedical anomalies, stochastic resonance, nano-oscillators for generating microwave signals and related complex systems. A common theme among these and many other related lectures is to model, study, understand, and exploit the rich behavior exhibited by nonlinear systems to design and fabricate novel technologies with superior characteristics. Consider, for instance, the fact that a shark’s sensitivity to electric fields is 400 times more powerful than the most sophisticated electric-field sensor. In spite of significant advances in material properties, in many cases it remains a daunting task to duplicate the superior signal processing capabilities of most animals. Since nonlinear systems tend to be highly sensitive to perturbations when they occur near the onset of a bifurcation, there are also lectures on the general topic of bifurcation theory and on how to exploit such bifurcations for signal enhancements purposes. This manuscript will appeal to researchers interested in both theory and implementations of nonlinear systems.
Nonlinear Dynamics And Chaos
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Author : Steven H. Strogatz
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Nonlinear Dynamics And Chaos written by Steven H. Strogatz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
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.
Deterministic Nonlinear Systems
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Author : Vadim S. Anishchenko
language : en
Publisher: Springer
Release Date : 2014-06-16
Deterministic Nonlinear Systems written by Vadim S. Anishchenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-16 with Science categories.
This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
Lectures On Chaotic Dynamical Systems
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Author : Valentin Senderovich Afraĭmovich
language : en
Publisher:
Release Date : 2002
Lectures On Chaotic Dynamical Systems written by Valentin Senderovich Afraĭmovich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Chaotic behavior in systems categories.
This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics. The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in.