Dynamics Of Very High Dimensional Systems
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Dynamics Of Very High Dimensional Systems
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Author : E. H. Dowell
language : en
Publisher: World Scientific
Release Date : 2003
Dynamics Of Very High Dimensional Systems written by E. H. Dowell 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 Technology & Engineering categories.
Many books on dynamics start with a discussion of systems with one or two degrees of freedom and then turn to the generalization to the case of many degrees of freedom. For linear systems, the concept of eigenfunctions provides a compact and elegant method for decomposing the dynamics of a high dimensional system into a series of independent single-degree-of-freedom dynamical systems. Yet, when the system has a very high dimension, the determination of the eigenfunctions may be a distinct challenge, and when the dynamical system is nonconservative and/or nonlinear, the whole notion of uncoupled eigenmodes requires nontrivial extensions of classical methods. These issues constitute the subject of this book.
Smooth And Nonsmooth High Dimensional Chaos And The Melnikov Type Methods
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Author : Jan Awrejcewicz
language : en
Publisher: World Scientific
Release Date : 2007
Smooth And Nonsmooth High Dimensional Chaos And The Melnikov Type Methods written by Jan Awrejcewicz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrence of both stick-slip and slip-slip chaotic orbits, research which is very rarely reported in the existing literature even on one-degree-of-freedom nonautonomous dynamics. This pioneering attempt to predict the occurrence of deterministic chaos of nonlinear dynamical systems will attract many researchers including applied mathematicians, physicists, as well as practicing engineers. Analytical formulas are explicitly formulated step-by-step, even attracting potential readers without a rigorous mathematical background. Sample Chapter(s). Chapter 1: A Role of the Melnikov-Type Methods in Applied Sciences (137 KB). Contents: A Role of the Melnikov-Type Methods in Applied Sciences; Classical Melnikov Approach; Homoclinic Chaos Criterion in a Rotated Froude Pendulum with Dry Friction; Smooth and Nonsmooth Dynamics of a Quasi-Autonomous Oscillator with Coulomb and Viscous Frictions; Application of the MelnikovOCoGruendler Method to Mechanical Systems; A Self-Excited Spherical Pendulum; A Double Self-excited Duffing-type Oscillator; A Triple Self-Excited Duffing-type Oscillator. Readership: Graduate students and researchers in dynamical systems.
Methods Of Qualitative Theory In Nonlinear Dynamics
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Author : Leonid P. Shilnikov
language : en
Publisher: World Scientific
Release Date : 1998
Methods Of Qualitative Theory In Nonlinear Dynamics written by Leonid P. Shilnikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.
Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced studentsof nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.
Extremes And Recurrence In Dynamical Systems
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Author : Valerio Lucarini
language : en
Publisher: John Wiley & Sons
Release Date : 2016-03-28
Extremes And Recurrence In Dynamical Systems written by Valerio Lucarini and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-28 with Mathematics categories.
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
Iutam Symposium On Nonlinear Dynamics For Advanced Technologies And Engineering Design
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Author : Marian Wiercigroch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-11
Iutam Symposium On Nonlinear Dynamics For Advanced Technologies And Engineering Design written by Marian Wiercigroch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Technology & Engineering categories.
Nonlinear dynamics has been enjoying a vast development for nearly four decades resulting in a range of well established theory, with the potential to significantly enhance performance, effectiveness, reliability and safety of physical systems as well as offering novel technologies and designs. By critically appraising the state of the art, it is now time to develop design criteria and technology for new generation products/processes operating on principles of nonlinear interaction and in the nonlinear regime, leading to more effective, sensitive, accurate, and durable methods than what is currently available. This new approach is expected to radically influence the design, control and exploitation paradigms, in a magnitude of contexts. With a strong emphasis on experimentally calibrated and validated models, contributions by top-level international experts will foster future directions for the development of engineering technologies and design using robust nonlinear dynamics modelling and analysis.
Statistical Physics Of Complex Systems
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Author : Eric Bertin
language : en
Publisher: Springer
Release Date : 2016-10-14
Statistical Physics Of Complex Systems written by Eric Bertin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-14 with Science categories.
This course-tested primer provides graduate students and non-specialists with a basic understanding of the concepts and methods of statistical physics and demonstrates their wide range of applications to interdisciplinary topics in the field of complex system sciences, including selected aspects of theoretical modeling in biology and the social sciences. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting units, and on the other to predict the macroscopic, collective behavior of the system considered from the perspective of the microscopic laws governing the dynamics of the individual entities. These two goals are essentially also shared by what is now called 'complex systems science,' and as such, systems studied in the framework of statistical physics may be considered to be among the simplest examples of complex systems – while also offering a rather well developed mathematical treatment. The second edition has been significantly revised and expanded, featuring in particular three new chapters addressing non-conserved particles, evolutionary population dynamics, networks, properties of both individual and coupled simple dynamical systems, and convergence theorems, as well as short appendices that offer helpful hints on how to perform simple stochastic simulations in practice. Yet, the original spirit of the book – to remain accessible to a broad, non-specialized readership – has been kept throughout: the format is a set of concise, modular and self-contained topical chapters, avoiding technicalities and jargon as much as possible, and complemented by a wealth of worked-out examples, so as to make this work useful as a self-study text or as textbook for short courses. From the reviews of the first edition: “... a good introduction to basic concepts of statistical physics and complex systems for students and researchers with an interest in complex systems in other fields ... .” Georg Hebermehl, Zentralblatt MATH, Vol. 1237, 2012 “... this short text remains very refreshing for the mathematician.” Dimitri Petritis, Mathematical Reviews, Issue 2012k
Dynamics Of Controlled Mechanical Systems With Delayed Feedback
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Author : H.Y. Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Dynamics Of Controlled Mechanical Systems With Delayed Feedback written by H.Y. Hu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Technology & Engineering categories.
Recent years have witnessed a rapid development of active control of various mechanical systems. With increasingly strict requirements for control speed and system performance, the unavoidable time delays in both controllers and actuators have become a serious problem. For instance, all digital controllers, analogue anti aliasing and reconstruction filters exhibit a certain time delay during operation, and the hydraulic actuators and human being interaction usually show even more significant time delays. These time delays, albeit very short in most cases, often deteriorate the control performance or even cause the instability of the system, be cause the actuators may feed energy at the moment when the system does not need it. Thus, the effect of time delays on the system performance has drawn much at tention in the design of robots, active vehicle suspensions, active tendons for tall buildings, as well as the controlled vibro-impact systems. On the other hand, the properly designed delay control may improve the performance of dynamic sys tems. For instance, the delayed state feedback has found its applications to the design of dynamic absorbers, the linearization of nonlinear systems, the control of chaotic oscillators, etc. Most controlled mechanical systems with time delays can be modeled as the dynamic systems described by a set of ordinary differential equations with time delays.
Multilevel Strategic Interaction Game Models For Complex Networks
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Author : Eitan Altman
language : en
Publisher: Springer Nature
Release Date : 2019-10-18
Multilevel Strategic Interaction Game Models For Complex Networks written by Eitan Altman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-18 with Mathematics categories.
This book provides a state-of-the-art overview on the dynamics and coevolution in multi-level strategic interaction games. As such it summarizes the results of the European CONGAS project, which developed new mathematical models and tools for the analysis, prediction and control of dynamical processes in systems possessing a rich multi-level structure and a web of interwoven interactions among elements with autonomous decision-making capabilities. The framework is built around game theoretical concepts, in particular evolutionary and multi-resolution games, and includes also techniques drawn from graph theory, statistical mechanics, control and optimization theory. Specific attention is devoted to systems that are prone to intermittency and catastrophic events due to the effect of collective dynamics.
Dynamical Chaos
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Author : Vadim Semenovich Anishchenko
language : en
Publisher: World Scientific
Release Date : 1995
Dynamical Chaos written by Vadim Semenovich Anishchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.
Dynamics And Self Organization Of Locally Coupled Neural Networks
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Author : Patrick Thiran
language : en
Publisher: EPFL Press
Release Date : 1997-01-01
Dynamics And Self Organization Of Locally Coupled Neural Networks written by Patrick Thiran and has been published by EPFL Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Neural networks (Computer science) categories.